{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "17f671ad-84e8-46dc-adea-ef5dd1365982",
   "metadata": {},
   "source": [
    "## Stochastic gradient descent\n",
    "\n",
    "SGD算法是一个特殊的RM算法\n",
    "\n",
    "mean estimation算法也是特殊的SGD算法\n",
    "\n",
    "那么这个SGD主要是解决什么问题的呢？\n",
    "\n",
    "它其实是用来解决**优化**问题的\n",
    "\n",
    "假设如下优化问题： $\\min_{w} J(w) = E[f(w,x)]$\n",
    "\n",
    "这其实就是求一个w，使得值最小\n",
    "\n",
    "---\n",
    "\n",
    "又一般说来，求一个最值问题，会需要把一个方程求导，然后令导数为0即可，当然，这样需要一点条件，不然导数为0，不一定能取得最值。\n",
    "\n",
    "在这里，同理这里需要一个极其苛刻的条件，**需要满足二阶导大于0**，这样通过使一阶导==0，就能得到全局最小值了。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10a58a19-3b5b-48d6-9500-28b8b2c2a7af",
   "metadata": {},
   "source": [
    "## Gradient Descent(GD)\n",
    "梯度下降，顾名思义就是函数往梯度下降的方向走，这样容易趋近最小值\n",
    "$W_{k+1} = w_k - a_k*\\nabla _wE[f(w_k,X)] = w_k-a_k[\\nabla _wf(w_k,X)]$\n",
    "\n",
    "在这个式子里面，其实w才是“未知”量，x是一个随机噪音，它通过采样获取。而w就是我们平常意义下的自变量，可以对它求导分析。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "356f7e96-986f-47ba-a84f-7b71adeca92e",
   "metadata": {},
   "source": [
    "那我们其实可以看出来，在$X\\equiv 0$时，其实那个$\\nabla _wE[f(w_k,X)]$可以退化成$\\nabla _wf(w_k)$ 也就是此时的所有的“梯度”，都是**真·梯度**了。不需要通过各种采样，把**真·梯度**给弄出来"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "61001fec-8414-4506-b82c-ac617b03b11f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "876e520d-01f0-4b85-844e-759beb38081a",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "有一丢丢理解了，$\\min_w \\ \\ \\ {J(w)} =E[f(w,X)] = E[\\frac{1}{2}\\left \\|  w-X\\right \\|^2  ]$这个式子想表达的意思是：\n",
    "\n",
    "$w$是变量\n",
    "\n",
    "$X$是在$w$取定之后，再随机得到的随机变量，其实得写成$X_w$\n",
    "\n",
    "然后这个是model-based的题目，也就是我是知道题目的方程是什么的。这题的目的，开上帝视角可以知道，这题其实目的是令自变量$w$不断接近于$E(x)$ \n",
    "\n",
    "那么轻易算得$\\nabla _wf(w,X_w)=E(w-X_w) = w-E(X)$\n",
    "\n",
    "那么这题其实过于简单只需要第一次就把$X$的期望算出来，后面就再也不用算了，这也就是传说中的**GD算法**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "id": "72dcc978-981a-43a6-995a-30e8147d3f30",
   "metadata": {},
   "outputs": [],
   "source": [
    "#这里我们基于梯度，通过RM算法求梯度==0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ccc4fd4a-3c89-4cc2-b88e-3a23300ce4a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b20143cd-e5b8-42a2-b721-ba7062ecb41e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# SGD\n",
    "X = np.random.randint(-10, 10,size =(1000,2))\n",
    "\n",
    "def train_mean_estimation(batch_size, note):\n",
    "    w = np.array([0,0])\n",
    "    results = np.array([[0,0]])\n",
    "    for i in range(0,1000):\n",
    "        batch = np.random.randint(0,1000,size=batch_size)\n",
    "        w = w - 1/(i+1)*(w-X[batch].mean(axis=0))\n",
    "        results = np.append(results,[w],axis=0)\n",
    "        \n",
    "    plt.figure(figsize=(8,3))\n",
    "    plt.plot(results[:,0],label='x')\n",
    "    plt.plot(results[:,1],label='y')\n",
    "    plt.yticks(np.arange(-5,5,1))\n",
    "    plt.legend()\n",
    "    plt.title(note)\n",
    "    plt.show()\n",
    "    #可以看到，得迭代很多次才收敛"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f2c8f0c5-32e5-4583-af19-39d5d5d2c7df",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_mean_estimation(batch_size=1,note=\"1-batch(SGD)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0b52d668-6be5-48dd-b4d6-296569c472c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_mean_estimation(batch_size=10,note=\"10-batch\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5f4ed742-b61c-46ea-b91c-14d58061d7b2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_mean_estimation(batch_size=100,note=\"100-batch(GD)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f603c9f-c60f-46f5-9595-22b34689cdc5",
   "metadata": {},
   "source": [
    "这里再弄一个新的例子，是用GD，MGD，SGD拟合 $y=x^2+5x+x$的方程\n",
    "\n",
    "我们这里定义损失函数 $loss = (y-\\hat{y})^2$ 即，均方误差\n",
    "\n",
    "然后对$loss$对$w$进行求梯度\n",
    "\n",
    "我们假设$w=\\begin{bmatrix}w_1\\\\w_2\\\\w_3\\end{bmatrix}$是三维列向量，表示函数的系数，$X=\\begin{bmatrix}x^2\\\\x^1\\\\x^0\\end{bmatrix}$也是三维列向量，表示样本\n",
    "\n",
    "于是$loss=(w^TX-A^TX)^2=((w^T-A^T)X)^2$\n",
    "\n",
    "那么我们知道，求梯度，其实就是对$w$的每个分量进行求偏导\n",
    "\n",
    "记$tmp=(w^T-A^T)X = \\hat{y}-y\\ \\ \\ $化简得$\\nabla loss = 2*tmp*X=2*(\\hat{y}-y)\n",
    "*\\begin{bmatrix}x^2\\\\x^1\\\\x^0\\end{bmatrix}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb5bdafc-a0c3-46cf-8a69-5f4f9dc01a8d",
   "metadata": {},
   "source": [
    "}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "48217219-bb2f-4cd9-a78a-658a330cbe86",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3efff5b5-bceb-49b1-b3c8-b7dedd841d4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 先初始化一个列表，未来要在这100个样本里面再sample出来\n",
    "np.random.seed(0)\n",
    "X = np.linspace(-10, 10, 1000)\n",
    "Y = 2 * X ** 2 + 3*X +5 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1a1a7d0d-44af-4f4e-adf3-171b20bfa2de",
   "metadata": {},
   "outputs": [],
   "source": [
    "#定义二次函数\n",
    "def quadratic_function(X, a, b, c):\n",
    "    return a * X ** 2 + b * X + c\n",
    "#定义损失函数\n",
    "def loss_function(Y_pred, Y):\n",
    "    return np.mean((Y_pred - Y)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "7acb8efa-02c0-4968-b0ff-703eefb437ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(learning_rate, batch_size, note):\n",
    "    # a,b,c就是上面所说的 [w1,w2,w3]\n",
    "    a = np.random.randn()\n",
    "    b = np.random.randn()\n",
    "    c = np.random.randn()\n",
    "    loss = 1000\n",
    "    cnt = 0 \n",
    "    results = np.array([0])\n",
    "    while loss > 0.01:\n",
    "        cnt += 1\n",
    "        batch = np.random.randint(0,1000,size=(1,batch_size))\n",
    "    \n",
    "        x = X[batch]\n",
    "        y = Y[batch]\n",
    "    \n",
    "        y_pred = quadratic_function(x,a,b,c)\n",
    "\n",
    "        loss = loss_function(y_pred,y)\n",
    "        results = np.append(results,loss)\n",
    "        # 这些是计算得到的梯度\n",
    "        grad_a = (2 * (y_pred - y) * x ** 2).mean()\n",
    "        grad_b = (2 * (y_pred - y) * x).mean()\n",
    "        grad_c = (2 * (y_pred - y)).mean()\n",
    "    \n",
    "        a -= learning_rate * grad_a\n",
    "        b -= learning_rate * grad_b\n",
    "        c -= learning_rate * grad_c\n",
    "\n",
    "        valid_batch = np.random.randint(0,1000,size=(1,5))\n",
    "        x = X[valid_batch]\n",
    "        y = Y[valid_batch]\n",
    "        y_pred = quadratic_function(x,a,b,c)\n",
    "        loss = loss_function(y_pred,y)\n",
    "        \n",
    "        # results = np.append(results,loss)\n",
    "    \n",
    "    print(\"最终系数为：\",a,b,c)\n",
    "    print(\"最后迭代次数：\",cnt)\n",
    "    y_pred = quadratic_function(X,a,b,c)\n",
    "    plt.figure(figsize=(8,3))\n",
    "    # plt.plot(X,y_pred,label=\"predict\")\n",
    "    plt.plot(X,Y,label=\"target\")\n",
    "    plt.plot(X,y_pred,label=\"predict\")\n",
    "    plt.title(note)\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    # print(a,b,c)\n",
    "\n",
    "    plt.figure(figsize=(8,3))\n",
    "    plt.plot(results[:150],label='x')\n",
    "    # plt.plot(results[:,1],label='y')\n",
    "    # plt.yticks(np.arange(-5,5,1))\n",
    "    plt.legend()\n",
    "    plt.title(note)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e642de6f-3558-4e15-8b1b-d1eacfb047cf",
   "metadata": {},
   "source": [
    "学习率调高了有概率收敛不了\n",
    "\n",
    "调节batch_size 从而确定GD还是SGD还是MGD\n",
    "\n",
    "若想使用SGD 调节为1即可"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "7231c145-855e-44b0-b744-b17d4dd30dfc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "最终系数为： 2.014503336479273 2.99896641076744 4.222936433155403\n",
      "最后迭代次数： 25120\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EREQMrWFgaUVPq+fiq1DvT0RERNQRMbSGga010wM8QitbBIiIiIgYWsPC0qqRV+7HW7jBABERERFDazjIg2dTiAuxPDcUsLE9gIiIiIihNRxasxDLq6eVlVYiIiIihtZwkAfNkBdieYRcbuVKRERExNAaFvKgabMLIS2m8txQgAuxiIiIiBhaw8J7bFXwl/htHu0AobYXEBEREXVEDK1h4DUBIITg6bUQi5VWIiIiIobWcGjNBgGex3JzASIiIiKG1rDwrKy2pj3AyukBRERERAyt4eB5id8cwqxWz4VYnlVbIiIios6IoTUMPKujofW0cuQVERERkSeG1jDwDJqh9KV6VlY9QywRERFRZ8TQGgatGXnlGXjZHkBERETUgtBaVFSEe+65B8nJyYiJicEll1yCnJwc6eOCIGD27NnIyMhAdHQ0xo4di/3797t9jqamJkybNg0pKSmIjY3FpEmTUFhY6HZMZWUlpkyZAqPRCKPRiClTpqCqqqpl32Ub8wyp5lBCKxdiEREREXkJKbRWVlbi8ssvh06nw48//ogDBw7g9ddfR5cuXaRj5s2bhzfeeAMLFy5EdnY20tPTce2116KmpkY6ZsaMGVi5ciVWrFiBTZs2oba2FhMnToTNZpOOmTx5MnJzc7Fq1SqsWrUKubm5mDJlSuu/4zbg1R4QwkIsr0ore1qJiIiIoA3l4FdffRU9e/bEhx9+KN3Wp08f6f8FQcD8+fMxa9Ys3HrrrQCAjz/+GGlpaVi+fDmmTp0Kk8mEDz74AEuWLME111wDAFi6dCl69uyJtWvXYsKECTh48CBWrVqFrVu3YsSIEQCAxYsXY9SoUTh8+DD69+/f2u87rLwXYrWip5XtAUREREShVVq/+eYbDBs2DLfddhtSU1MxZMgQLF68WPp4Xl4eSktLMX78eOk2g8GAMWPGYPPmzQCAnJwcWCwWt2MyMjKQlZUlHbNlyxYYjUYpsALAyJEjYTQapWM8NTU1obq62u1Pe2lNT2trZrwSERERdVQhhdYTJ07g3XffRb9+/fDTTz/hoYcewvTp0/Gf//wHAFBaWgoASEtLc7tfWlqa9LHS0lLo9XokJiYGPCY1NdXr66empkrHeJo7d67U/2o0GtGzZ89QvjVFec1pDWlzAW7jSkREROQppNBqt9tx6aWXYs6cORgyZAimTp2KBx54AO+++67bcSqVyu3vgiB43ebJ8xhfxwf6PM8++yxMJpP0p6CgINhvS3GtqZayp5WIiIjIW0ihtVu3brjwwgvdbhs4cCBOnToFAEhPTwcAr2poWVmZVH1NT0+H2WxGZWVlwGNOnz7t9fXPnDnjVcUVGQwGJCQkuP1pL60aeeXshxWzuYXTA4iIiIhCC62XX345Dh8+7HbbkSNH0Lt3bwBAZmYm0tPTsWbNGunjZrMZGzZswOjRowEAQ4cOhU6nczumpKQE+/btk44ZNWoUTCYTtm/fLh2zbds2mEwm6ZhI5rkhgMUa+kKsKK0GANsDiIiIiIAQpwc8/vjjGD16NObMmYPbb78d27dvx6JFi7Bo0SIAjkv6M2bMwJw5c9CvXz/069cPc+bMQUxMDCZPngwAMBqNuP/++/Hkk08iOTkZSUlJeOqppzB48GBpmsDAgQNx3XXX4YEHHsD7778PAHjwwQcxceLEiJ8cALimBUTrNGiw2ELqaRXvG6VTo8FiC2nyABEREVFHFVJoHT58OFauXIlnn30WL730EjIzMzF//nzcfffd0jEzZ85EQ0MDHn74YVRWVmLEiBFYvXo14uPjpWPefPNNaLVa3H777WhoaMC4cePw0UcfQaPRSMcsW7YM06dPl6YMTJo0CQsXLmzt99smxOpojF7jDJ6hLMRyHBul0wCwSH8nIiIi6sxUgiB0yFJedXU1jEYjTCZTm/e3Xv36epw4U4ceidEorGzA328YgAevOi+4+762HifO1iEzJRZ5Z+vw9IT+eOR354f5ERMRERG1vVDyWsjbuFLzxBX/MXpH5TiUS/wWt0orpwcQERERAQytYSEuxIp2Bk9zCNu42mQ9rQDYHkBEREQEhtawsDh7WqOlSmsIC7E8pgdYOD2AiIiIiKE1HMRKa4zesc4ttM0FxPYAsdLK0EpERETE0BoGVq9KawvmtOpCr9ISERERdVQMrWEgLcQSe1pbsI1rNBdiEREREUkYWsNA3IpVqrSGsBBLvK9BDK1sDyAiIiJiaFWaIAiuHbFasBDL1R7g+NF4bglLRERE1BkxtCpMvnAqRicuxAquWmqzCxC3eohmpZWIiIhIwtCqMHnIFDcXCLanVV6RjWJoJSIiIpIwtCpMHjJDbQ+QV2nZHkBERETkwtCqMHnIjAkxtMonBbDSSkREROTC0Kowi4/gabEGFzwtsi1bxR2xWGklIiIiYmhVnDiySqtWQa9xnN5ge1rF9gCNWgWdVuX8fKy0EhERETG0Kky8xK/VqKDTOk5vsO0B4nEatQpatdjTytBKRERExNCqMLEyqlOrodM4qqWh9rTq1Cpo1WKlle0BRERERAytChN7ULUaV3tAsHNaxcCr1aihDfG+RERERB0ZQ6vCLDZX8NSJPa1BbuMq74cVK6029rQSERERMbQqTR48dZrQelrl/bDaEFsLiIiIiDoyhlaFWWTBU68NsadVbA9Qq6WFWKy0EhERETG0Kk7saXUsxAqxp1XWDytWWjnyioiIiIihVXE2u2zkVYhzWl2VVldPK9sDiIiIiBhaFWeRXeKX97QKQvMVU6mnVXZftgcQERERMbQqTmoPkI28EoTgwqe4jatWo4JGqrQytBIRERExtCpMDJnyrVjltwdicxuXJY68YnsAEREREUOrwqSRV7I5rUBwfa3ycVkabuNKREREJGFoVZi0FavGtZgKCG5BlTQuS74Qi5VWIiIiIoZWpclnrapU8q1cmw+fYt+rTsOFWERERERyDK0Kky/Ekv/XYg1iIZbzvhq1+0KsYCYPEBEREXVkDK0Kk4+8AgCdNvhZrVa7q7VADLsAq61EREREDK0KEyutGqnSGnx7gLy1QCPrh+WuWERERNTZMbQqTFqI5QydofS0ygOvfPIAQysRERF1dgytCrPIRl4Bsp7WoEKrK/DKJw/YOPaKiIiIOjmGVoXZZCOvHP919rQGsRBLag/QuLcHcOwVERERdXYMrQrzWojVgvYArVoFlcpVbeUGA0RERNTZMbQqTAqeYqVVG3xolQKv877if62stBIREVEnx9CqMNcEAHEhVvA9rTZpG1e1239ZaSUiIqLOjqFVYRab50IscU5rED2tNvfAy0orERERkQNDq8I8R15JPa3WINoDbK6FWIArvHLkFREREXV2DK0Kk08AAEJbiCW2B4iTB9geQEREROTQqtA6d+5cqFQqzJgxQ7pNEATMnj0bGRkZiI6OxtixY7F//363+zU1NWHatGlISUlBbGwsJk2ahMLCQrdjKisrMWXKFBiNRhiNRkyZMgVVVVWtebhtwnMhll4bfE+ruBBL49UewNBKREREnVuLQ2t2djYWLVqEiy66yO32efPm4Y033sDChQuRnZ2N9PR0XHvttaipqZGOmTFjBlauXIkVK1Zg06ZNqK2txcSJE2Gz2aRjJk+ejNzcXKxatQqrVq1Cbm4upkyZ0tKH22bEgKlTh97T6prx6tEeEETgJSIiIurIWhRaa2trcffdd2Px4sVITEyUbhcEAfPnz8esWbNw6623IisrCx9//DHq6+uxfPlyAIDJZMIHH3yA119/Hddccw2GDBmCpUuXYu/evVi7di0A4ODBg1i1ahX+7//+D6NGjcKoUaOwePFifPfddzh8+LAC33b4iBVVjWdPa1CVVtecVsDVYmBhewARERF1ci0KrY888ghuvPFGXHPNNW635+XlobS0FOPHj5duMxgMGDNmDDZv3gwAyMnJgcVicTsmIyMDWVlZ0jFbtmyB0WjEiBEjpGNGjhwJo9EoHROprH52xApmIZZ4X6k9wPlfG9sDiIiIqJPThnqHFStWYOfOncjOzvb6WGlpKQAgLS3N7fa0tDTk5+dLx+j1ercKrXiMeP/S0lKkpqZ6ff7U1FTpGE9NTU1oamqS/l5dXR3Cd6Ucz4VYoc1p9WgPEO/LkVdERETUyYVUaS0oKMBjjz2GpUuXIioqyu9xKpXK7e+CIHjd5snzGF/HB/o8c+fOlRZtGY1G9OzZM+DXCxerxyX+UHpaPVsLxOkBNrYHEBERUScXUmjNyclBWVkZhg4dCq1WC61Wiw0bNuCtt96CVquVKqye1dCysjLpY+np6TCbzaisrAx4zOnTp72+/pkzZ7yquKJnn30WJpNJ+lNQUBDKt6YYq8diqlC2cZUWcWnc2wO4uQARERF1diGF1nHjxmHv3r3Izc2V/gwbNgx33303cnNz0bdvX6Snp2PNmjXSfcxmMzZs2IDRo0cDAIYOHQqdTud2TElJCfbt2ycdM2rUKJhMJmzfvl06Ztu2bTCZTNIxngwGAxISEtz+tAeLx8irUBZiubaA9WgPYKWViIiIOrmQelrj4+ORlZXldltsbCySk5Ol22fMmIE5c+agX79+6NevH+bMmYOYmBhMnjwZAGA0GnH//ffjySefRHJyMpKSkvDUU09h8ODB0sKugQMH4rrrrsMDDzyA999/HwDw4IMPYuLEiejfv3+rv+lwcgVP55zWEHpaPWe8Su0BXIhFREREnVzIC7GaM3PmTDQ0NODhhx9GZWUlRowYgdWrVyM+Pl465s0334RWq8Xtt9+OhoYGjBs3Dh999BE0Go10zLJlyzB9+nRpysCkSZOwcOFCpR+u4qTg6Tmn1dp88BRbC7wrrWwPICIios6t1aF1/fr1bn9XqVSYPXs2Zs+e7fc+UVFRWLBgARYsWOD3mKSkJCxdurS1D6/NuaYHtKQ9wHellTtiERERUWfXqm1cyZsSC7G0as+FWAytRERE1LkxtCrMc1erUHpaxQVXWo85rdzGlYiIiDo7hlaFWT2CZyhzWm3OwKvzmPHKhVhERETU2TG0Ksy1EKv127iK/+XIKyIiIursGFoVZmnFQiyptUCq0rI9gIiIiAhgaFWcze6+EEuvDb6n1WZz3xFLw4VYRERERAAYWhVn8dMeEExPq1il1ag9R16x0kpERESdG0OrwrxGXoUyp9V5jM6rPYCVViIiIurcGFoV5rlBQGibC7jPadVwcwEiIiIiAAytihIEQVrpr5HmtIY+PcC1BSwXYhEREREBDK2Kks9T1YnB07kQK5ieVs8qLRdiERERETkwtCpIHi5b1R7gcV/2tBIREVFnx9CqIHlolUZeBRlabXYBgvPuYnuA2Ntq4fQAIiIi6uQYWhUk7z312hGrmdAqH2vl2R7AbVyJiIios2NoVZB8u1WNFFpdW7EKgv/wKW8B8Ay8bA8IzG4XYGewJyIi6tAYWhUkLaRSq6BSOYOn1nWKLQHCp3todbYHaILfTauzstkF3LhgE257f0vANwX+rDtUhiVb88PwyIiIiEhJ2vZ+AB2JNLLKGTYBV08r4Aifeq3v9wlu7QHSjlhsD2jO2domHCypBgDUmW2IM4T2lH76i904W2vG7/p3RY/EmHA8RCIiIlIAK60KEhdiieOuANclfiBwxVS8r1oFqD22cbUwtPpV22SV/r+m0RLSfQVBQEWdGQBQWRfafYmIiKhtMbQqSFyIJa+0atQqODMozAFCq0W6r+tHIn4eG6cH+FXbKA+t1gBHemuy2iG+H5CHXyIiIoo8DK0KskjtAe6n1TVBwH/F1CZVaV2BV6q0ciGWX3WtqLTK71tvZmglIiKKZAytCpIvxJILZitXz+1fAVelldu4+lcjC57VIVZa65ps0v+z0kpERBTZGFoVZPGxEAtwTRAI1B4gBl55DywXYjVP3h5Q3RBipVVWXZUHWCIiIoo8DK0KsvlYiAW4ZrWaA1RafU0e0AbRVtDZyYNnqD2t8pYAtgcQERFFNoZWBflaiAUEtyuWOD1Aq2alNRQ1rViIxfYAIiKicwdDq4IsPoInIOtpDbi5gHfgFUOrhdMD/GrNQqx6t/YAhlYiIqJIxtCqIDF46lpVafVuD+A2rv65z2lteaW1zsyeViIiokjG0KogXxMAAECndfa0BgqtNrYHtIT7nNbWLMRipZWIiCiSMbQqSBp55W9Oa6CRV3Yf7QHO/w9Uoe3sFKu0MrQSERFFNIZWBUnTA/y2BwTYXMDHxgTi/aystPpV6zanteU9rVyIRUREFNkYWhVk8XGJH5AvxGp+Tqu8p1VsM+DmAv7VKVRprWdPKxERUURjaFWQ/4VYzfe0ugKv677ivFdWWv2raUVoZaWViIjo3MHQqiB/I6+CmR7gai1w3VcjbuPK0OqX245YIbYHyIMqe1qJiIgiG0OrgsRKq8bPNq4BF2KJ93WrtLI9oDnysFnbZIU9hIAvbwmo5zaurVZc1YAvdxZy4SAREYWFtr0fQEcijq3SeYy8CmpzAR+LuMRFWXYBsNsFqD0+b2dntwtu81UFwTHGKj5KF9T95YG3zmyFIAhQqXiOW+r/fXcAP+4rRYxei+uy0tv74RARUQfDSquCpA0CvEZeBTGn1e4941X+/2wR8CafsypmzVD6WuWVVrsANFhYbW2NvLN1AIASU0M7PxIiIuqIGFoV1KodsWzeM17ln8fKrVy9iD2pWrUKiTF6AKH1tcpDL+A+TYBCV1rdCACobmB/MBERKY+hVUGKLMTyU2kN1FrQWYmLsOKitEiIcnS6hFRp9QipXIzVco0WG6rqHW8YQl0QR0REFAyGVgW5qqUePa3a5ntaXVvAyiqtsv/nVq7exEprrF4r9bGGspWrZ0jl2KuWK6tukv7f1MDQSkREymNoVZDU06r2M6c1wPQAX60FarUK4qfiBAFvYsiMj9IiPsRKqyAIUntAvMFxX1ZaW+50TaP0/9UMrUREFAYMrQqy+OhLBYLsaZUWcbkHXi03GPBLDJlxBldorQ4ytDZZ7RBPadd4AwDuitUapSZZaGV7ABERhQFDq4J89aUCwYZWcRtX9x+JGGKt7Gn1IlZVYw2htwfIq6opztDK9oCWO10tr7TyPBIRkfJCCq1z587F8OHDER8fj9TUVPz+97/H4cOH3Y4RBAGzZ89GRkYGoqOjMXbsWOzfv9/tmKamJkybNg0pKSmIjY3FpEmTUFhY6HZMZWUlpkyZAqPRCKPRiClTpqCqqqpl32UbkbZi9ai0BjWn1cc2roBrMZaF0wO8iCHTsRDLEVqDDUxiVTVap5EWcbE9oOXkoZU9rUREFA4hhdYNGzbgkUcewdatW7FmzRpYrVaMHz8edXV10jHz5s3DG2+8gYULFyI7Oxvp6em49tprUVNTIx0zY8YMrFy5EitWrMCmTZtQW1uLiRMnwmZzXZ6dPHkycnNzsWrVKqxatQq5ubmYMmWKAt9y+PhbiBXKnFZ/rQVciOVNDJnxBnlPa3CBSVrEZdAgRu8MrWwPaLFS2UIstgdQZ2Wx2VEmewNHRMoKaUesVatWuf39ww8/RGpqKnJycnDVVVdBEATMnz8fs2bNwq233goA+Pjjj5GWlobly5dj6tSpMJlM+OCDD7BkyRJcc801AIClS5eiZ8+eWLt2LSZMmICDBw9i1apV2Lp1K0aMGAEAWLx4MUaNGoXDhw+jf//+SnzvipN2tfIceRXENq5S4FV79rQ6K61ciOWlpkneHhDaQqx6s+u+sVyI1WrySqu4nS53cKPO5onPduP7PcX48bGr0D89vr0fDlGH06qeVpPJBABISkoCAOTl5aG0tBTjx4+XjjEYDBgzZgw2b94MAMjJyYHFYnE7JiMjA1lZWdIxW7ZsgdFolAIrAIwcORJGo1E6xlNTUxOqq6vd/rQ1MVhqWtDTavG7EMvxd1ZavckXYiWE3NPqqKrG6LWIM2jcPh+FTh5aBSG0eblEHcX+IhPsAvDbsbPt/VCIOqQWh1ZBEPDEE0/giiuuQFZWFgCgtLQUAJCWluZ2bFpamvSx0tJS6PV6JCYmBjwmNTXV62umpqZKx3iaO3eu1P9qNBrRs2fPln5rLSYtxPKc0xpET6vNJt7XcyFW8/ftrKTNBVpTadXL2wMYtFpCEAS30AqwRYA6p8p6MwDgQEnbF02IOoMWh9ZHH30Ue/bswSeffOL1MZXKPbQJguB1myfPY3wdH+jzPPvsszCZTNKfgoKCYL4NRflbiCUG0UA9reJCK88qrWt6ANsDPMkXYrmmBwQXPKVKq0GLOKk9gD2tLVHdYEWjxfH8NEY7fg5cjEWdjd0uSM/7/cUMrUTh0KLQOm3aNHzzzTdYt24devToId2enp4OAF7V0LKyMqn6mp6eDrPZjMrKyoDHnD592uvrnjlzxquKKzIYDEhISHD709ZcY6t8L8QKOPLKz/QAtgf4VytvD4gObSGWvNIq9rRy5FXLiBsLGKN1SHWOD2OllTqbmkarNPv5WFlNwM1kiKhlQgqtgiDg0UcfxZdffolffvkFmZmZbh/PzMxEeno61qxZI91mNpuxYcMGjB49GgAwdOhQ6HQ6t2NKSkqwb98+6ZhRo0bBZDJh+/bt0jHbtm2DyWSSjolEVj+X+KWFWAFCq6u1wKM9wLmoy8LQ6qXWbXMB58irICuttbKe1lj2tLaKuLFAekIUEqLF0WMMrdS5iK0BgOOq29GymgBHE1FLhDQ94JFHHsHy5cvx9ddfIz4+XqqoGo1GREdHQ6VSYcaMGZgzZw769euHfv36Yc6cOYiJicHkyZOlY++//348+eSTSE5ORlJSEp566ikMHjxYmiYwcOBAXHfddXjggQfw/vvvAwAefPBBTJw4MWInBwDyHbH89LRa/QdPf4u4gmkPKKpqQHpClNd9Ozrxcn6cbBvX2iYrbHah2XMhVlrjDBrEcuRVq4j9rKkJBunKADcYoM5GHloBR4vAoAxjOz0aoo4ppND67rvvAgDGjh3rdvuHH36I//mf/wEAzJw5Ew0NDXj44YdRWVmJESNGYPXq1YiPd43/ePPNN6HVanH77bejoaEB48aNw0cffQSNRiMds2zZMkyfPl2aMjBp0iQsXLiwJd9jm5FmrbZoRyzfi7jEz+VvG9dtJ8pxx6KtuG9Ub7x4c1bLHvg5StoRS+8KrYAjuIq9lf7Ie1o58qp1xNCanhAl9W2zPYA6m6p69+f8Afa1EikupNAqCM1folapVJg9ezZmz57t95ioqCgsWLAACxYs8HtMUlISli5dGsrDa3eu0Oq5ECuEzQW8tnF1/N3fNq77nL8YO2Pjf22T40UiPkoLg1YDvVYNs9WOmkZLs6FV3tMax9DaKqedGwukJURJYZXtAdTZeFZaOUGASHmtmtNK7vzviBVEpdXPfV2VVt/3rahrcv7X7PPjkcrUYMHZ2qbmD/TDarNLK9bF0JkQwtgrsRUgRq9FDHtaW6XUWWlNM0ZJ83I5PYA6G7HSen5qHADgYHE17FyLQKQohlYF+VuIpdc2P2vVNT0gtEqrGFZbEwDbmiAImLRwE65+bb1U8QyVfDxVrBRagx97VS/bxlWqtJptQV1NIHdie0BavEGa4hDsgriWsNkF/O93B7B6v++ZzUTtocpZaR3eJxF6jRo1TVYUVja086Mi6lgYWhVk8TvyKohtXP3NaW2m0nq21vGLsrrRes5s9VrdYEV+eT2qG1v+S73WGXb1WrX0psC1wUDzVb5a2RawYui12QU0dbAxNYIg4O11x/DLIe8RckqRelqNUVJbRjjbA7JPVuD/NuVhzg8Hw/Y1iEJV6ay0do0z4IJ0R7X1QImpPR8SUYfD0Kogq9/NBYLvaQ11IZa8LaDyHGkRKJXtnnSmpmUVYvluWCLX2KvmA1O9sz0gVq9FjM61ALCjtQjsLTLhnz8dxqyV+8Ly+a02u/QzTEtom/aA4irHGx2xl5YoEog9rV1i9Liwm2NOeGdca0AUTgytCpL6UtV+Rl4F2hGrmd20mmsPAIDyzhRanYuw3ENrKD2tjmNi9Bqo1SrE6MW+1o419irvbB0AxzkPx65q5XVm2AXHFYKUOINrTmsYpweIYbXBYutwbzLo3CX2tHaJ0UmhlRMEiJTF0KogaQKAR7XUoHUEIrsANFl9hyKbn9YCsV3AX+Atl/WyniuLsUpNrpaAlvbiipsDtDS01jvvL7YGdNRdsU6V1wMABMHVSqIkcWOBrnEGaNQqqdIazjmtp2Vves6lXm7q2MRKa2KMHoO6O+azcoIAkbIYWhVk9bOrVXyUVrrs7y84+N3GVeN/G1ez1e624OVceQEvNbkeZ3u1B8grrfLPU9fChWGRKr+iXvp/eYVbKdIirATH9q3GNqm0MrRS5JFXWgekO+aSl5gaz5liAtG5gKFVQRY/7QFqtQpd4xwv6mV+goOrSuvRHuCcJuCrp9VzLuC58stRifYA8bJwnGxTgWCnBwiCIN1frLC62gM6Vmg9JQutp8MaWqMAQJoeUG+2hW1h4Gm358+58Zynjq9KVmmNj9Khd3IMALYIECmJoVVB/kZeAUBX54t6mZ+Q5q8fViNt4+odWstrz83Q6hY6Wlgpq2nyVWkNrj2gyWqH+B7Asz2go/W0iu0BgP83TK0h31gAcFW7gfBNEJAvwGrp84dISWarXZr9nBijBwAMynD2tXKCAJFiGFoVJI6l8uxpBRwzLAH/wcHipx9WF2DklWdIPVcWYpWYlJseEOsjtDYXluTV1GidR3tAB6q0NlpsblXtcKy2L5WNuwIcPdjxhvDNarXbBZTVyNoDWvj8IVKSWGVVq1y/h7gYi0h5DK0KEQRBmgDgOWsVAFKdPX/+Kq02P/2wGrX/jQnK69w/V0UYFtqEgxI9iWLvaXyUd09rc3NaxXFX0TqN9LOS2gM6UE+r5wzccPa0pjrflAGQJgiEY+xVRb3Z7d8Ce1opEogzWo3ROqidv1MuzODYKyKlMbQqRN5yqlN7n9a0eGd7gJ9ql9j/5xl4ddJCLP+VVvGYc6E9oMlq8xrT1ZJRTGILQKxe3tMaXHuAGExjDa75rB2x0nqqos7t7+HsaRUrrUDwFe/WfD0RQytFAnk/q+jCbo4JAsfP1KLR0rHajojaC0OrQuSLTny1B4iV1tM1fhZiif2wXtu4iiOvvCutYvjLTIkFAJyti/wXcDG067VqqFWOUUwV9aGHbV8LseKDXIgl9q3GyAKva+RVx3lxEftZxRDp7w1Ta3j2tAII66xW79Aa+W/UqOOrlE0OEKUlGBCr18AuAEVV3M6VSAkMrQqRr+73tRArtZlKq81PT6vYHuBr5JX4gt0v1TFe5VyotIr9rOkJUUiKdQT5lvS1ivNU42U9reLK9ebaAzwnBwBArLM9oL4DtQeI466G9U4EoHx7QKPFJrUAyEOraytX5c+lGJLFqnpLe6KJlOSr0qpSqdA9MRoAUNTC7aqJyB1Dq0Lkl7g9JwAAzfe0WvxsLhB4IZbjc/VLc+xzXVVvCcuuR0qSFu4kRKFrfCtCq8+FWI6wVGe2+Qz5IjGYikFV/nk60uYCBc7QOjwzCYCjx1TJy5TixgJROrUUIgGEdStXsdI6KMNx6ZXtARQJXJVWvdvtGV0cobWYlVYiRTC0KkR++d7nQixnpbW8rskrWNrsAgTn3T3ntGqCaA84r2scVM4vKf7yjFSnTa4eyJQ4xy/4llzirfXZHuD6/9oALQJSe4DBuz2gY/W0OkJrVoYRUTrH80rJFoHTsjcgKpXrOS9WvMPZHpDV3bHIpd5s61DVcTo3iZVWeXsAAHRnaCVSFEOrQqTL+2qV2wu4KDlWD41a5XM7TXkV1Xvklf/2AHHEVUqcQbosFektAvIRSa2qtEpzWl3VUp1GLYWzQIHJd6VV3FygY/S0CoIghdbeyTHS5Xt/PdUtIf4sU2WtAYC8PSAcodXxXOnbNU76WZ/lBgPURvLL63DVvHX4ePNJt9tdW7i6h1ax0lrI0EqkCIZWhUi7YflYhAW474rluZhEvnGAv21cfe0uJAbU5Dg9kmIdobU8wi+XipeU01rZHiAtxDK4v0gEs5WrOATcbSGWvmNt43qmpgmNFjs0ahUyukRL0ytKTcqFVrFqm+4RWhOkn4Hy57JU1hOd4vz3xA0GqK38cqgMpyrq8UVOodvtVX7aA1hpJVIWQ6tCxIVYvsZdifz1tbqHVo/pAWrfO2JZbHbpF2VSrCy0niuV1oQoKcS3JHTU+GgPAILbFcu1EKvjjrwSF2FldImCTqN2Ta9QcDFWYaXja3Tr4hFawzinVdxYIE0eWrkYi9rIybN10n8FwfU7WfxdnOgZWhPF0Kr8uDmizoihVSHWZiqtgGsAe5nHJVq39gCvSqvaeYx7aBUvR6lUjl+UybHnSHuAybs9INRdjcxWO8xWxzmL07uH1oQgxl6JLQCxPntaO0Z7gDjuqleSY//z9Ga2EW6Jk86vkZkc63Z7QpjmtFpsdqm1Ji3BIIVWLsaitiI+52uarG4FgubaA0pMDbAHWBxKRMFhaFWIuFDKcyGVnNj757mdphhI1SpIu6mItH6mB4jhNDHG0SubHBf5lVb5FpzpxpZXWuXVUHm1FJBXWlvY09pB2gPESmuvJEeglHpaFay0nix3VJ16e4RWY5jmtIqBW6dRITFGj67x4kK+zh1azVY7/vThdrz47f72figdnvicB1xVV0C2I5ZHaE2LN0CjVsFiE9jGQqQAhlaFiKFS52NygChV6uF0Dw6ufljvH4dW2hHL/V26uGWr2BYgzjytiOANBsrrHFtwqlSOc5HSwp5WcRFWlE7tdc6CqrT66mntYO0BBRXulVaxPUCpnlaLzS5tE9snJcbtYwlhWojl2jI2Cmq1ipVWp71FVVh3+Aw+/O0kKiP4Teu5Tv6cB4A8Z2gVBMHnnFbA8TtdvMrBDQaIWo+hVSFitVQTsD3A9wYD8skDnsQeV8+FWGJFVQytydJCrMh90RJDR3KsATqNWqq0mhosaLIGf1m+1s8iLCDISquPnlYxtFpsQkiPJVKdqghve0BRZQNsdgFROrW0yEuUINtcQN7311qnpUV8jueNq70kcp/zbeFYWa30/9knK9rxkXRshc7nvEisutY2WaXf/56hFXD0lQPcYIBICQytCvG3Datcmp+tXKXWAp+h1fdCLGlygFRpjfz2ALHK1825T70xWgedM+SHEral3bA8FmHJbwu0cl1sAZBXWmN0rgBb3wH6WvPLXeOuAPf2ACWCpNQakBTr1dIitgeYbXY0WZXb7OK0bFwaAE4PcJKH1m15DK3hIm8NcPzd8W9MXIRl0KoRrdd43Y8bDBAph6FVIcEtxPJdaZVaC3y2B/heiCWOtvKstEbyQixxcoAYoOSXeENpEXDthuX9AhEvtQcEGHnlDKVxsoVYWtmM13N9V6x6s1W6ZN4zyT201ptt0uQFAPg0+xQGz/4J20MMO2I/nxiK5WL1Gog5VskWgVLnvxvx3xHbAxzkoTXUn2Nr7SsyYdW+kjb9mu0l3/mcj3EGU/HfgL/JASKOvSJSDkOrQizSJf7mR16drW1yu8wkVlF97aQlhmDPhVjl0oxWx+dMijsHQqs0OcAg3daS4OFqD/CutCaEVGl1D73S2KtzbDFWo8Um9bACrtYAY7ROqnpG6zXSuSmTLcZavu0Uahqt+PC3vJC+plhl6pMS6/UxlUoVlrFXZV6VVudCrE4+8urYGVdo3V9sCstOZL4IgoCpS3Lw0NKd+O3Y2Tb5mu1JfM6PPi/F8Xfn2KtKP7thicRKa3M9raYGC9YdLlO0pYaoo2FoVYhYadUFqLQmx+qhVgF2wX0TAGnGq69Ka5DtAcnOhViV9Wafu2dFAvmMVlFLNhgIFFrjg1iIVe9j5BXgahc41xZjzfxiD66ctw6f7ygA4Bp35VkFTfOYXlHTaMG+4moAwLrDZSFth5rvvFTaJ9k7tALyDQaUC1Cna9x7WsWFfHVmGxrM535LR0s0WmzS4qDEGB3sApBzsrJNvnZhZYMUxJZvP9UmXzMUSoc/sT3gqgtSoFY5nndnapuaDa3irNaiZma1vvz9Afzpw2z8d2eRgo+aqGNhaFWIJUC1VKTVqKXKqHxBTKDWArFy69Ue4LEQS5wPKAiumYGRxtWTGC3d1rUF7QF1AUOr4zZTgHPgr9J6Ls5qtdsFrDtcBgCY9dU+7CmskiqtYmuAyHPs1Y78SukNTqPFjvWHzwT9dcWe2T4+2gMA+Vauyr0BkHZTc7YHxBu00GudW7lGYIvAV7uKMPzltdh5Knwh8sSZOgiC43xfMzANQNv1tcq/r9X7SyNmNz6LzY7r5v+KmxZukn63KkFsBzg/NU4KoifP1ivSHiAIAn494qhWbzwa/L9Dos6GoVUh0gSAAHNaAd8bDEiTBwK1B9h8z2kVK61ajVp6px+pLQLyLThFKc5Zm6EsphGrqJ67YQHAealxAICDpTVotHiHT0EQUG/2XWmNE2e1nkOV1hNn66TzYbbaMXVJDnYVVAEAenuEVmnslTO0bjvhCDfi8+6HvcH1JlptdikY9/bRHgAACdFim0ZwldavdhVhwPM/4pdDp/0eI/aCpznbA1QqVat2VQu35dtO4UxNE/7jsU+9ksTWgPNT4zCibzIAYFteedi+ntyuU1XS/1tsAr6MkArhviITDpXWYF9RNXYXmhT5nPJxV5kpsdIVhpNn6/xu4SoS2wNMDRa//fJFVQ3Sv8uc/LaplBOdixhaFeJaTOW/0gp4X6IFAk8ecG0u4GchVpzrF2VSGMZeKXmJzVdPa9dW9LR6hk4A6JsSi7QEA8xWO3b6+OXfZLVLbzA8K61ie4BSC7F2F1S59Y+Gwy5ntWtQRgL6psSixNSI7/c4wmcvj9Aqjb1yPve2nnCEm3tG9ALg2FfdV9D3VFzVCKtdgF6rRjfZGxA5sT0g2J7WFdmn0Gix4511x31+vK7JKi0gS3N70+NdqTdb7Tgh6/NsD2arHbsLqwAA64+cUbTiJycuwjq/axxGZCYBAPYWmkJq9WgpsdI6sq/j667IPhUR/Zjy0LfhiDJVy+KqBljtAgxax4g3MbTmldf53Q1LFGfQSlce/FVb5Y+5sLJB0U1AiDoShlaFuMZWBVlplYVWi91/e4DY5yrvabXZBVQ5w4DYy+r4f2UXY72z/hj6P7fK5zt/q82OaZ/swqyVe4PqofUXOro6L/W2pD0g3kdoValU0kKJzce9K07yKmqM3rPS6vh7vQL9kT8fPI2b3/4N9/57e1hfyHOdVdXR5yVj0b1D3Xb58gyt8vaAuiYr9hY5qlB/ubIvuneJRr3ZFlSLgGvcVYzXuCuRMYQNBhotNux0Vu125Fe67TQkEl/E4wxat7aQruJiLNmbnjk/HMTVr2/Aj0FWjsPhQEm1NO6rqt4iVb+VdrzMVWntkRiNDGMUrHYBO/PD8/VEjRYbDjj7oWdPGoRonQbHz9RhRwRUCXecVD60ihsJ9El2jHgTFyA6Kq2+NxaQa24x1g6PPmRWW4l8Y2hVSDALsQDf7QG2AHNaNT62ca2sN0PMQfJ390lSaG39pVJBELBs6ymYbXYs3Zrv9fHfjpfj293FWLbtFF5ffbjZz1cqCx3iYinAtQI8lNBaE6CnFQBGnee4TLr5uPeKZjGQRus0Xu0Y4ggtsdJaYmrAvf/eHvRlc1GjxYbZzi01D5XWIDuMC2PES7RDeiXi/NR4vH77xdLHMru6X7qX5gRXN0r9rD0So9EzKQbXZ6UDAH4MYnxRvp/tW+WkDQYCLIiTfw9m2TzX/+4s9DpGvDIhtjiIpOkTzg0G7HYB3+4uBgB8kl3Q7NcOF8/Q8fPBsrB8nWOy0KpSqXCZs9q6PcwtAnuLTLDaBXSNN6B/WjxuurgbAOCTdl6QJQiCW3DeU1ilyJt4z7nHmc5d4PLO1vndwlWuezMbDIiPWZxh7RliiciBoVUhwYy8AoBUX+0Bdv/buOo03u0B4i/hLjE6t/uIW7meVaA9IO9snVQVWHvwtFuoAOBWxXpn/XF8t6c44Ofz3M1IJO1qFMrmAo3+2wMAR9URAHYXmrwu9YuLsHzNePXcyvWtn4/i1yNn8NK3B0KayPDehuMoqHC9OK0I0wt5g9mGw6drAACX9OwCALguqxveuftSzPvjRegmW/AGuLembHO2BozIdJyr6wc7QsfPB5tvEcg7G3gRFuAaPWaqb77SKrYpiG+6vtxZBLvH+T7tY/IE4D0ybX9xtbRI8bdjZ9utv1u8dD6wWwIABOzVbSmrzS5VAM939nKLfa1bw7wYS2y9ubRXF6hUKtx5maPF5Ie9JYqOOQvVqYp6nK1tgl6jRt+usRAEZRY2SZVWZ4VVbA/IL6+XtQf4r7QGWoxV3WjBoVJH1fr+KzIBADlhXLzXWo0WW1BtREThwNCqELHSGmgbV8BVaT3jYyGW70qrd3uA2LMqvsiLUhSc1brxqKtKWdNodataWm12/LS/FAAwyvki+fTne6TLhb6USP2s7qFDDK21Tdag+/DqAuyIBQA9EmPQKykGNruAbI8Xb3EygGdrAADE6l3tAeW1TdLomdLqxqBf+Aoq6vHuekdfpvgC9H2YXsj3FplgswtISzBIFRoAuGFwN9w+rKfX8WnSVq6N2OIMimI/4pCeXZCeEIXaJis2HfWuUMtJ4678LMIC5JXW4EPrtKvPR3yUFkVVDdJtotMeG1OIXG96HKF1/WFXRdNmF7BqX2mzXz8cxFA345p+0KhVOHK61m2WrhIKKhtgttkRpVNLoUistOYWVIU1WMgr/IDj+dM/LR6NFju+zg1uQZapwSL1ZCtFrFBmdU/AtRc6piko0SLgOeKtZ1IMNGoVGiw2qdrtr6cVCLwr1q5TVRAERzvPhEGOKx77i0wROcat3mzFtW9uwHXzf43Ix0cdH0OrQsRKnC7AyCvAVWl1H3klTh4IsI2rrD3Ac3KAKEnBntZfnb/oxR5JMaQCjpE6lfUWJMXq8dGfh+PKfilosNjwwH92+P3arhmt7tW/OIMWBnFsUZB7yNc0U2kFXNVWzxaBej/jruSfr7bJiiVb892qy5/tCO5S84vfHkCT1Y7R5yXjuRsH4oK0ODRZ7fgmyBfyUIgv+Jf0dFS7miMGPItNkHphRzrfdKjVKlznbBH4oZkWgZPNzGgFZD2tzYTWRotNCkBj+6fiposzAABf5Li3CHjupiby3FFNDCjnOVsjxFaBtlRc1YASUyM0ahWu7JeCYb0dwe7ng8pWW8Ww1DclTuot7psSi5Q4x0LE3Qr10R4/U+t2pUEQBKmSfKkztDqqrY43Ssu3Bbcga+qSHbjlnc2K/ozEy+zD+iRhzAVdAQC/HjnrVbkPleeIN51GjR7OsVdiy5G/6QFA4J7WnJOON9bDeieiR2I00hIMsNoF7HEu5IskX+cWo6CiASfL67EiO/Jm81LHx9CqEGkhVjMjr8TL42dqmqRfpBZxTquP1gJfC7HK69y3cBVJ0wNa2dNqttqlStyMay4AAKzef1p64fre2RowYVAaDFoNFt51KXonx6CoqgFPfpbr8wXLNaPVvT1ApVK5NhgIYoLAzlOV0iXxnon+L0+7+lrdK3aBZryKI68q6sxYssXRx/vw2PMAAGsOnG72zcC6Q2VYe/A0tGoVXrp5kOOFfLjjsukn2wsUX5AlBk+x2tUcnUYtVeMFwXHJUnzhBYAbL3K0CKw5cBpNVt9VFJtdkFoffG3hKpI2F2hmTuvOU5Uw2+xISzCgT3IM/ji0BwDgx32lbq0d0rgrr55W10IsU71FClMv3zIYgGP8k7x/vC2I/awXdktAjF6LcQNTAQA/H1K2r1XezypSqVQY0Vfsa219i8Bn2QUY9/oG/OPrfdJtRVUNKKtpglatwuDuRun2W4Z0R7ROg0OlNVh9IHBAzz5Zga3OkWtvrjmi2HSFnHzH5xzaOxHDeichRq/B2domHCjxfxWoOfIRb/KrC55v2gJVWsW5rsU+NhgQg/bQPolQqVQY6nyTE2ktAoIg4D9bXOsbFv96QnrtImorDK0KCXYhVkqcASqVoyWgwtkLJVVpfdxXIxt5JYYesT1A3KhAJE4SaG2lNSe/EvVmG1LiDLhvdB90idGhvM6M7XkVsNkF/OS85Hp9liPkGGN0WDRlGPQaNdYdPoMffVySLfExo1UU7K5YdruA2d84Fjj9cWiPgJenxdB6oKQalbLzIbUH+AitYsvAr0fOoLzOjO5dovHEtRcgq3sCLDYBX+3yXy2VL7768xWZOD81HoDjhVyvUeNASTX2FbX8hdMXMbSK/azBkFcqR2QmuVVoh/ZKRFqCATWNVtz/0Q6fLQ3FVY5L0nqNWqoe+SLOaW2uLUIMLqP6JkOlUmFIzy7omxKLBovNbQGcv/aAFFlP9KZjZ2EXHCFuZN9kXNKzC+wC8OPetm0REEOrGD6uHuAc+n+iQrFxaoDv0ApAGn21+sDpVr1RstrseOuXowAcO16J7T9iZXxgtwREy65YdInRSy0x//zpcMA+cLGFBnDMGv46t/XVVlO9BUdOO87J0N6J0GvV0iSR1rQIiCPeDFq12+8vz55u8eqCL2L7Rml1o1tAt9rs0r/jYb2TnI/d8d+22tksJ78Sg2f/hLfXHQt43I78ShwsqUaUzvHmt9jUqMjPraMzW+04WFKNlbsKMfeHg3jis1xp10IKHUOrQoJdiKXTqJHkvIwkVo/E+/raXEAeZMUXgebaA1o7p/VXZ//mlf1SoNeqpZ12ftpfiu15FSivM8MYrZOCIQD0T4/HQ86q5Ivf7keN7LJwTn6F1GvYt6v7Cywgu8TbTKX1i5xC7Ck0Ic6gxczr+gc8NjU+Cv1S4yAI7sPWxfaA2ADtAWKP8f+M7gOtRi31h362w3+19M01R5BfXo/0hChMH9dPuj0xVo8Jzsvunyh4Oa3U1IgSUyPUKuCiHsbm7+DkFlqdFTmRWq3CvD9ejBi9BpuOncWt7/wm9fKJxMukPZOiA+7+Fmx7wFapt9bxXFKpVPiDs9oqtgjY7UKz7QG1TVascrawjHVeFp7orBw3t0hQadKlc2doPa9rLHonx8BsszfbLxwK+cYCcjcM7gaDVo29RSbpTUFLfL+3RBqoLwiOUWLurQFdvO7zwFV9YYzW4VhZLb70MQUCAA6WVOOXQ2VQq4C7nC0Fb/1ytNXVVvFxZTpbJABgTH/Hc6E1oTVPmpbhPuJN/qY5Pkob8Cpb1zgDdBoVbHYBp2Vvzg+W1KDebENClBb9nD9HeaU13HNvBUHA3B8OoqbRijfXHMHxAPONxSrr7y/pjr9c2ReAY9Fpa1sv2kp7zBDOya/EZXPW4vp/bcTjn+7G+7+ewJc7i/Cnj7YrusV1qBotNvy0v9RrgfW5gKFVIYG2YvUkTRBwXrZ03dfH5gKy26weodWzPSDZeam0st7cql8k4qKjqy5wVCnEcUir9pXi+72OADD+wjSpdUH08Njz0Cc5Bqerm/D66iMAHJW5qUt2wmITcN2gdGnhllwwlVZTgwWvrjoEwLG4JTXe91B7udE+WgTqzP4XYslbBmL1GtzhfEG9+eLu0GvVOFRaI802ldtdUIXFG08AAF6+Jcur9eCu4Y7P801usWJD33MLHC/Q/dMTfH4v/sgvr4/08bMYc0FXfP7QKKQnROH4mTr8/u3fkH3SFXyC6WcF5O0BFr8vFo0WG3KdVTv5Y7n10u5QqRyXt/vN+gF9//6DFJ482wMSorTQO5+Hq8XQ2t9xOV5sd8g+WRlwC82ztU2KvfA2mF3zS8XwoVKpcPUAx2NSaoqAIAjSjNbzPN4IpsQZcNswR/B/b4PvzRqC+fxiNfSOYT2h16ix6dhZrD9yRpqpK4ZyOWO0Tmqpmb/2qM82k/edj+n6wd3w/MQLkRyrR355Pb4McCUDQLMTPHbIWgNEY/o5QuvO/MoWhwR/I97koTXQ5ADA8YZQnOYhfy6Kj/nS3olSIB6UkYAonRpV9RYcP+M9s1hJW06US+0JVruAl78/6PO4sppGrHL2uk8Z1Rt3j+iFhCgtjpXVNtsKEgn+vSkPI+f+HPQiQSVYbXb8/cu9qKq3ID5Ki8syk3DfqN7oZnT8bp2xIjekqTRKevqLPZi6JAezVu5tl6/fGgytCgk0AcCTNEHAWWkNtIhL/vnE/iF/Pa3iL067AGnzgVCdrW2SLmNfcb7jF/7l56cgzqBFaXUjPtvhqJ7c4AwEclE6Df7f77MAAP/ZchLZJyswdUkOztY2YUC6Y4aor2H0weyK9a+1R1FeZ8Z5XWNx76g+QX0vo3xsMlDf5H/kVYzstjuG95KClzFGh+ucq3o9F2Q1WW14+ovdsAvA7y/JwDhnVVpuZN9k9EqKQW2TFTO/2IPPdhRgX5HJb99oMMRLtKG0BgCuSmV6QpTX5gOiQRlGfP3o5Rjc3YjKegvu/WA7jjr7iIOZ0Qq4pgfYBdcbBU878x39rOkJUW79sd2M0bjB2XpikfVyD+5u9BrjJe+JbrLaEa3TYHhmovR5hvdx/L+/Wbvf7SnGyDk/Y8q/tynSn7ensApWu4D0hChkyCY6iFcrfjl0RpGAXFbThNomK9QqoE+K98/xwSvPg1rlqDB6TvU4eroGX+QUBqxsrj9yBodKaxCr1+DvNwzE/1zeBwDw8vcHcaDY8cZtSE/fvdT3je6DtAQDiqoasGyr+9WFgop6fOvcse2vY85DjF6Lh8Y4Qu5bPx/1+zP4dncxLnlxNWat3Ov3/ImTA4bJQmuv5Bj0TYmF1S5g8zHfs2vLa5uw+bj/xVqujQXcz3Nmsjy0+m8NEGU4Z7W6h1bvx6zTqHFRjy4A4HNXPyX9a62j/WPcgFRo1Sr8cqjMZ1V6xfYCWGwChvZOxKAMI+KjdNLv4XfXH1Okimm2OiZPFFYqe+l8X5EJL/9wEKermzDj01x8HuSi2tZatu0UDp+uQZcYHTbO/B0+mzoKL96chUVThsGgVeOXQ2V4LYgZ58FotNiw4OejePHb/c1ODdlw5Iy0+PHznELFNuBoKxEfWt955x1kZmYiKioKQ4cOxcaNG9v7IflkDXIhFuC9wYD4wqwJsI0r4Aq3Uk9rrHvVSa9VS/MxW7rBgHj58sJuCVIYiNJp8DtnpchstSM+SovLnYHQ05X9umLSxRmwC8DkxVuxt8iExBgdFt87zO9qf19bccrtKzLh4y0nAQAv3DQIem1wT9uRfZOgUjl6/8TtVANVWsVL2moV8Cfni7ToDme19OvcYrdfCm+vO44jp2uRHKvHP24a5PNxqNUqTHZulfrdnhLM/GIPJi7YhCEvrfF7CXV3QRWOOIOiL7ukRVhd/B7jy8XSPNf0gBMH0hKi8NnUURjVNxkNFhseWb4TDWaba0arj6AkZ9CqpQqov919tsrGbnk+lgV3DcHGmb/Dlmevxo7nrsGe2ePx9SOX+2xJSJFtZTz6vGQYtK43H+I0AjEoyR0rq8HML/bAahfw27FyvPaT/xeQerMV3+4uxkNLcvDo8p1+e3XFxTNDeye6fU/D+yQhzqDF2domLNvmvVkH4HgDFOwbGbGftXdyrNv3K+qVHIMbnLN33//VVW3dV2TCLe9sxlOf78aslfv8hg2xynrXZb1gjNHhkbHno0uM47K/xSYgJU6Pnkm+e5qjdBo8Ns6xgPPtdcfc+ngX/XoCNruAK/ulIMu5iOuekb2REmdAYWWD19QIAFh3uAyPf5qLmiYrlm07hb/7CK4Wm2vb3GF93MP0Vc52kS9yCtz6281WOxb/egJj/7kekxdvw5Of7/YZmqXJAR499D0So6Xfz4EmB4i6d3H8m3G1XAjYIU4O6OPeqiNWi8VKrC+tffOz9UQ5tuVVQK9R439vycJ9o/sAAP7fdwfczoPFZpees/eO6i3d/qfL+yBKp8buQpPP3QdDYbHZMe2TnXhsRS4mLtgk9fm2ltlqx1Of74bNLiA13gBBcFQZl28L7+SDijoz3ljjuNr45Pj+bs+PwT2MmPfHiwA4/p21tvq7+fhZXDf/V7y+5gg+/O0kZn6xJ+DVree/ciyqFK9aPfvfPW7tfJEuokPrp59+ihkzZmDWrFnYtWsXrrzySlx//fU4dSryRm2II6maG3kFuA95BwIv4tK4VVoDtwcArsVZLe1rlfpZL3APpWKLAABce2FawOD43MSBiI/SwmIToFWr8M7dQ9HTT1UPcFVaC5yDwUV7CqvwyPKdmLRwE2x2AeMvTJNegILRJUaPQRmO4e7f7imBIAiy6QHeL/R9U2Ix7erzMffWwV6Pd1TfZHTvEo2aRituXvgb/vbfPXh/w3G841y88OLNg3z+PET3X5GJ+Xdcgj9fnolRfZPRJUaHerMNT3y2G2+vc1UqGi02/OPrfbj57d8w/s1f8cSnuV6Xtq02O/YWitWuLkGfDwD4Xf9UrJpxJZ69YUCzx0brNXjrriHoGm/AkdO1eOGbfV7zKv1RqVQYfb7jkv+fP8rGol+Pe/0ilRZhnefdpqBWq9AzKQbdjNFIiTMgIUrnd8vYFNmCxLH93Z8f12d1g1rleBOwZGu+9Bjqmqx4aOlO1Jtt6OsMI+//ekJqMRDtOlWJ6Z/swrD/XYtpn+zCqv2l+G5PCe54f4vPqQRiZczzzYReq8aDVzn6AJ//er9bOBMEAR/9lodLXlyD/s+twvCX1+LmhZvw16U5eGf9MWzPq/Cqnhzz0xogJ1Ywv9tTgoKKehRU1ON/PsyWQuSnOwrwprPSJpeTX4nteRXQaVS4/0rHwipjjA7Tr3b1ag/plRjwTc9tw3ogMyUW5XVm/OnD7Zjzw0F89FuedKXir84WAsDxPPur1FJwBOsPl0k/p5z8Cvx1aQ6sdkeVT60CVmQX4Pmv3QP3/uJqNFrs6BKjQ98U93MyfpCjyr32YBlGzPkZ0z/ZhRXbT+G6f/2Kl384KO2wt3JXEf66dKfXufbXEqPVqKXfE8FUWrt7VFoLKxtwutoxheFiZ2VVJFZefb3hs9sdz5eLX1qNP324vcXTMRY4F9ndNqwHuhmjMX1cPyTF6nGsrNZtF8Q1B07jdHUTUuIM0uJbwPFac4ez3/8fX+8L2A8biNVmx4xPc/HTfkebQVW9BZMXb1Wk//vd9cdxqLQGSbF6fD/9SvyPM5j/feVefLApL6jgLy6kCmXu8eurD8PUYMHAbgmY7Nx4Q+7mS7pL/z5nfrEH72047tVfarML+O3YWby34Tie+CwXNy3YhEteWo3r5v+Kx1bswtvrjuHpz3dj8uJtOFlej9R4A7RqFb7ZXYz5Pv5dA8DCX47hVEU9uhmj8N20K9ErKQbFpka88uMht+OsNrt0dS3SBN8M1w7eeOMN3H///fjLX/4CAJg/fz5++uknvPvuu5g7d247Pzp3wY68AlxbUW4+fhbTPtklDcD31Q+rUqmgVatgtQuw2QXY7YK0A4u8wiRKitUj72ydtCtQIPnlddh2ogLJcXqMOi8Z0TqNtKmA2AsmGtu/K6J0ajRa7NKlW7/fX3wUXrp5EJ5buQ/PT7zQZyiRE9/xHSqtwbD/XYuUOD1S4gw4VOr6R3PVBV3xv7dkNfs9ebr8/BTsK6rG//vuAJZtzYf4K8pXpVWlUuHJ8b4XeKnVKvzlyky8+O0BHD5dI43dAhyjv24cHPic6DRq/H5Id/x+SHcAjheeV1cdwvu/nsA/fzqMElMD7hzeC49/moujZa5f/l/uKsL3e0vwwJV9ccul3dG9SzSOn6lFg8WGeIM2YGjxZ0B6QtDHdo034F93XoJ7/m+b1BoCNB9aAeDtyZfi7yv34uvcYsz54RC251Xg+YkXwhitgwoqr1mxLSUPrWMuSPV6/HcM74VPtp/C81/tw46TFZhzy2A8++VeHCurRWq8AZ9OHYX3NhzHB5vy8OTnu/F9umNV/KurDrmFy15JMbguKx1f7izCodIa3PbeFiy9f4QUXARB8JocIDft6vNRUWfGR5tPYuYXuxGlc6xun/nFbqyVbfN6pqYJZ2qasLvQJE3i0GvUuLinEbde2gOTLs7wOzlALqu7EVf2S8HGo2fx+urD2F1oklp1/nBpD7z8w0G89fNRpCUYcPcIVwVN7IP9/SXd3dox7hnZG//ZchIny+t9fn9yOo0aT0/oj4eX7UT2yUq3rYwv6dnFq7f97hG98PHmkzjlDNaX9uqCO4f3wv9+fwCNFjvG9u+KxfcOw3d7ivHEZ7uxbNspaNUqzLjmAnSJ0UkVy6G9Er3e3Iw+LwXz77gEizeewP7ianyzuxjfOC+PpsTpMXPCACTF6vHI8p1Ye/A0/vRhNhbfNwwalQonzro2hfA1raRPcgzyztYFVWkVp21sy6vAU5/vlp4rg7ob3aYwAK75t8fP1OHD3/Jw08UZSIkzoKCiHk9/sVt6w7fu8BlcP38j/nnbRbh6QBoEQcDGo2fx0eaTOFZWi9/174o/Du2JrO4Jbm8ydpyswG/HyqHTqKQ3DMZoHZ4cfwFmrdyHN9ccQfbJChwqrcFJZ3vEXZf19CpW/HXs+fhhXymOn6nDpAWbMOfWwbj5ku7NnguRzS44/s3tKYFOo8L8O4ZgRfYpbDx6Fn/+KBv/uvMSabe+UB0qrcbCdY7wNnvSIHSNN+CFmy6EXqvGol9PSK8J943ugz8O7eF1JfBYWQ0+zS7Af3cWocK5+PjmSzLwx6E9MLi70e+btv3FJmk749k3Xeh3werTE/oj72wtftp/Gq/8eAif7yjASzdn4fzUOHyWXYAV2QU+5/pW1VvcXhsB4J6RvTDzugH4cW8JnvnvXvzr56Po2zXW7WdxrKxGuurywk2O8/HKHwZj8uJtWLbtFG68qBtS4gz4b04hVu4qQqPFhu2zrkGUzrvA055UQnssqQuC2WxGTEwMPv/8c9xyyy3S7Y899hhyc3OxYcOGgPevrq6G0WiEyWRCQkLwL9It9fTnu/F5TiFmXtcfD489P+CxP+0vxdQlOV63v3bbxdKcSrkBz/+IRosdd13WC3EGDRZvzAMAHH35eq/FUA/8ZwfWHDiNYb0TkRirR0WdGWarHWkJUcjoEoVuxmiUmhqw4cgZnJSN3dBr1LiohxE78isRrdMg94VrvS47fp1bhMOlNXhyfP+AK8dDZbMLeO6rfdh8/CxOVdRDfEZq1SrcdHEGHriyLy7MaNnPsLy2CfNWHca3e4qlIeAA8OofBuOO4d7vgJtTWFmPvYUm7C1y/LELAt6845KgFob58uFveXjpuwOQ/ytMiTPgtdsuQmKMHi9/fxDbT7pfIozVa1BntuGK81Ow9C8jWvR1Q/WvtUfx5lrH5S6tWoVD/++6oN6gCYKA5dtP4cVvDsDs49JrN2MUNv/t6qA2R/Dnnz8dwtvrjqNvSix+eWqsz8eweOMJvLrKMYYpJc6As7VN0KhVWPHgSAzvkwSLzY47F21FTn4l+iTHoLzWLFXg/nBpD0wZ1RsX93C8UOWX1+GeD7ahoKIBqfEGzLpxIGL1WpgaLHjy893Qa9XYN3uCz6sRdruAv6/cixXZBdCqVegSo5e2HX32hgG46eIMlJoaUVzVgPzyeuw85Qh88isQsXoNDDoNKurMfn9niDYdPYt7Ptgm/b17l2h8+fBopCVE4Y01R/DWz0ehVjkqn0WVDcg5VYmCigaoVMCax6+SRreJDpVW48udRZg+rp/PWceethwvx+HSapyqaEBBZT2q6s149oaBUiiTO1vbhPfWH8eSrfloklWdhvVOxJL7R0jB7oucQjz9xW7p30xClBYqlQqmBkuzv3/3FpqwfPsp7DhZgbH9u2LauH5S7/rWE+X4y8c7UNtklf6NiQxaNQ6+dJ1XIH5zzRH86+ejeHHSIOnyuj8bj57BlA+2e93+wk0X4k+XZ3rdfvPCTdjtvKKiUaswsm8Sdp2qQr3ZhmidBo9efT6+3V0sBZibL8nAviKTz8VbA9LjMbZ/KhKitYjVa/F1bhF2nqrCXZf1xNxbL5KOs9kF3PjWRq9Q1DMpGv99aLS0iFiurLoR01fskoL05BG9MP7CNKhUKqjguAopvhFz9WKroFY5qs2bj5dDq1bh3XuG4toL09BkteHxT3Pxw95SqFTAwPQE9EuLQ7/UOHSNN6Csugkl1Y0oNTVCBUebRs+kGPRIjHFbqzBv1WHsLTLh2gvTsGjKUOl3jCAIeP/XE3j7l2PSv/F4gxaX9k6EzS7AbLOjusE9GOo0Krf++r4pseifHo/eyY7JIAlROlQ3WlDdYME3u4uxv7gaEy/qhoWTL/U6X3J2u4D/7izEKz8ekgpNapVjLQDg2Kr9yn5dcUFqHPqlxTsqo1UNOFJWgyOlNWiw2PCXK/tiuKy9ZO4PB/H+ryeg16jxyh8GS2/qF/5yDNtPVmDcgFT8333DpPMxa+VeLNt2Cnqt2q3amxijw5L7R0htPOEUSl6L2NBaXFyM7t2747fffsPo0aOl2+fMmYOPP/4Yhw+79581NTWhqcn1i726uho9e/Zss9D6+Ke5WLmrCLNuGIgHnJcB/Wm02PDcV/tgswu4IC0e/dPjMLBbgtciE9HIOT9LI39EKXF67HjuWq9jX/h6Hz6WDYAORKtW4ZKeXVBa3Sj1WQHA7/p3xYd/uiyoz6G0erMVR0/X4lRFPS7tnSjNN2yt2iYrvt9TjE+zC3CyvB6fPjgS/dLim79jG/hxbwke+zQXZqsd4wakYt4fL5LaPARBwE/7T+PdDcdx7HSN2wvps9cPwNQx5/n7tIqy2QXc++9t+O1YOTJTYrHORzgMZF+RCU9/sQfHymrcfvn/dex5eOa65lsVAhHDwN+uHyBdcvNlx8kKPLp8l/Rv6bkbB0qjewCgxNSAG9/aJLXfXNTDiBcnDfK5ecPp6kbc+8F2t4q7aHifRHz+0Giv20U2u4AnP8vFV84Zl+d1jcVbdw3BoAzfLw6CIOBURT1+2l+KT7YXSAuDAOCrRy4PuBhPEATctHAT9hVVIzFGhy/+OlqqzguCgGe/dARoOZXKMQnk6Qmt+7m0VFlNI95bfwJLt+XjgrQ4LLt/JIwel99X7irEaz8d8apEff3I5VLfdkvsLTThvg+3S8+BxBgdMlNi8cehPaW+dLlGiw078ysxPDPJq4Dgqclqw4wVuag323BxDyMu6tEFF/Uw+gyCAFBVb8aXO4vwdW6RFF4Bx1a9r/3xYvRKjkGjxYZ5qw7j37/lSR+PM2hx27AeGJGZhO/3lvodbaRRq7D+qbFerVDHymqxZMtJdE+MRv/0BAxIj0dqvCHgG0urzY5//XwUC9cdQ6iJQqNWYeFdQ9wqqja7gOe/3tfq3lNjtA5rHr/K5zmubbLivzmF+GjzSbd/U/LH9bv+qbhzeE9cdUFXbMsrx+c7CvHT/lK3N1W+ROnU+OXJsQFnWcuZGix4c80R/GfLSdgFx++QySN64fqsbiFXOu12AQ8tzfE51SFKp8aax8e4/cxrGi2Y8OavKDY1QqtW4XcDUvGHS3vg6gGpQa8faa0OFVo3b96MUaNGSbe//PLLWLJkCQ4dcu/BmD17Nl588UWvz9NWofXVVYew7lAZHryqL2691H/loyVy8ivwy6EyWGwCzFY7rHY7xg1Mw+/6p3odW1zVgKVb82HQapAcp0dKnB5atRol1Y0ocW4vGWvQ4Mp+XTH6vGTER+kc43PO1GH94TIcKKnGX65oeWWTWubI6RoUVtbjd/1T/b44CIIAU4MFhZUNqGuy4tLeic2+UCrpTE0TXvhmH669MA23DGn5c9xis6PRYoPVJiAxQB9wKKobLYg3aJut2JbXNuHVVYfQNd6Ap8b39zp+x8kKzF97FDde1A13DOvpt48WcISKl78/iBNn65ztO3aoVSrMuKaftKGAP1abHa87F2pMu/r8oMeWCYKALSfK8Vl2AaL1Wrz8+6yAjxFw9OW+ve4Ypo/rJ61Klz+Ol747gJPl9bi0VxcM7Z2IS3p2QXxU8z2a4dZosUGrVgWs6DeYbThVUY+T5XWIM2hx+fm+F4iGorbJiuNlteiVFKPY87O18s7WYfX+UqQmGHDzxd29fubrD5dhyZZ8XNkvBX8Y2sPt52eqt+D7vSU4XFqNerPN+ceKay9M9xnEW2PDkTN4x7n4ThAAAYBG7bh6lBpvQGp8FOKjtBDgCKaCIODy81P87upXUFGPQ6U1OFpWg2Ona1FeZ0ZaggHpxmh0M0bBLjh26CuorEdhZQOanH2nKpUKOo0K06/uh2suDPxv0W4XsPl4OYpNDdBr1NBp1NBrHVcePedCA46AmZNfgZNn63Gqoh55Z+vQYLYhIVqLhCgd4qO0uPbCdFzRL/TnYqmpEU1WW7PTWZpTb7biha/3Y79scohGrcKfLu/jM5+cKq/HjvwKjLmgq9emRW2hQ4TWUNsD2rvSSkREREShCSW0Ruz0AL1ej6FDh2LNmjVut69Zs8atXUBkMBiQkJDg9oeIiIiIOoaInh7wxBNPYMqUKRg2bBhGjRqFRYsW4dSpU3jooYfa+6ERERERURuK6NB6xx13oLy8HC+99BJKSkqQlZWFH374Ab17927+zkRERETUYURsT2trtfXIKyIiIiIKTYfoaSUiIiIiEjG0EhEREVHEY2glIiIioogX0QuxWkNs1a2urm7mSCIiIiJqD2JOC2aJVYcNrTU1ju0Ve/bs2c6PhIiIiIgCqampgdHoeztrUYedHmC321FcXIz4+Phmt3ZUgrgDV0FBAacVBIHnKzQ8X8HjuQoNz1doeL6Cx3MVms56vgRBQE1NDTIyMqBWB+5a7bCVVrVajR49Wr4/ektxN67Q8HyFhucreDxXoeH5Cg3PV/B4rkLTGc9XcxVWERdiEREREVHEY2glIiIioojH0KoQg8GAF154AQaDob0fyjmB5ys0PF/B47kKDc9XaHi+gsdzFRqer+Z12IVYRERERNRxsNJKRERERBGPoZWIiIiIIh5DKxERERFFPIZWIiIiIop4DK0Keeedd5CZmYmoqCgMHToUGzdubO+H1O7mzp2L4cOHIz4+Hqmpqfj973+Pw4cPux0jCAJmz56NjIwMREdHY+zYsdi/f387PeLIMnfuXKhUKsyYMUO6jefLpaioCPfccw+Sk5MRExODSy65BDk5OdLHea5crFYrnnvuOWRmZiI6Ohp9+/bFSy+9BLvdLh3Tmc/Xr7/+iptuugkZGRlQqVT46quv3D4ezLlpamrCtGnTkJKSgtjYWEyaNAmFhYVt+F20nUDny2Kx4JlnnsHgwYMRGxuLjIwM3HvvvSguLnb7HJ3lfDX33JKbOnUqVCoV5s+f73Z7ZzlXwWBoVcCnn36KGTNmYNasWdi1axeuvPJKXH/99Th16lR7P7R2tWHDBjzyyCPYunUr1qxZA6vVivHjx6Ourk46Zt68eXjjjTewcOFCZGdnIz09Hddeey1qamra8ZG3v+zsbCxatAgXXXSR2+08Xw6VlZW4/PLLodPp8OOPP+LAgQN4/fXX0aVLF+kYniuXV199Fe+99x4WLlyIgwcPYt68efjnP/+JBQsWSMd05vNVV1eHiy++GAsXLvT58WDOzYwZM7By5UqsWLECmzZtQm1tLSZOnAibzdZW30abCXS+6uvrsXPnTjz//PPYuXMnvvzySxw5cgSTJk1yO66znK/mnluir776Ctu2bUNGRobXxzrLuQqKQK122WWXCQ899JDbbQMGDBD+9re/tdMjikxlZWUCAGHDhg2CIAiC3W4X0tPThVdeeUU6prGxUTAajcJ7773XXg+z3dXU1Aj9+vUT1qxZI4wZM0Z47LHHBEHg+ZJ75plnhCuuuMLvx3mu3N14443Cn//8Z7fbbr31VuGee+4RBIHnSw6AsHLlSunvwZybqqoqQafTCStWrJCOKSoqEtRqtbBq1ao2e+ztwfN8+bJ9+3YBgJCfny8IQuc9X/7OVWFhodC9e3dh3759Qu/evYU333xT+lhnPVf+sNLaSmazGTk5ORg/frzb7ePHj8fmzZvb6VFFJpPJBABISkoCAOTl5aG0tNTt3BkMBowZM6ZTn7tHHnkEN954I6655hq323m+XL755hsMGzYMt912G1JTUzFkyBAsXrxY+jjPlbsrrrgCP//8M44cOQIA2L17NzZt2oQbbrgBAM9XIMGcm5ycHFgsFrdjMjIykJWV1enPH+D43a9SqaQrITxfLna7HVOmTMHTTz+NQYMGeX2c58qdtr0fwLnu7NmzsNlsSEtLc7s9LS0NpaWl7fSoIo8gCHjiiSdwxRVXICsrCwCk8+Pr3OXn57f5Y4wEK1aswM6dO5Gdne31MZ4vlxMnTuDdd9/FE088gb///e/Yvn07pk+fDoPBgHvvvZfnysMzzzwDk8mEAQMGQKPRwGaz4eWXX8Zdd90FgM+tQII5N6WlpdDr9UhMTPQ6prO/DjQ2NuJvf/sbJk+ejISEBAA8X3KvvvoqtFotpk+f7vPjPFfuGFoVolKp3P4uCILXbZ3Zo48+ij179mDTpk1eH+O5cygoKMBjjz2G1atXIyoqyu9xPF+O6sSwYcMwZ84cAMCQIUOwf/9+vPvuu7j33nul43iuHD799FMsXboUy5cvx6BBg5Cbm4sZM2YgIyMD9913n3Qcz5d/LTk3nf38WSwW3HnnnbDb7XjnnXeaPb6zna+cnBz861//ws6dO0P+vjvbuRKxPaCVUlJSoNFovN7xlJWVeb0z76ymTZuGb775BuvWrUOPHj2k29PT0wGA584pJycHZWVlGDp0KLRaLbRaLTZs2IC33noLWq1WOic8X0C3bt1w4YUXut02cOBAafEjn1vunn76afztb3/DnXfeicGDB2PKlCl4/PHHMXfuXAA8X4EEc27S09NhNptRWVnp95jOxmKx4Pbbb0deXh7WrFkjVVkBni/Rxo0bUVZWhl69ekm/8/Pz8/Hkk0+iT58+AHiuPDG0tpJer8fQoUOxZs0at9vXrFmD0aNHt9OjigyCIODRRx/Fl19+iV9++QWZmZluH8/MzER6errbuTObzdiwYUOnPHfjxo3D3r17kZubK/0ZNmwY7r77buTm5qJv3748X06XX3651/i0I0eOoHfv3gD43PJUX18Ptdr9171Go5FGXvF8+RfMuRk6dCh0Op3bMSUlJdi3b1+nPH9iYD169CjWrl2L5ORkt4/zfDlMmTIFe/bscfudn5GRgaeffho//fQTAJ4rL+20AKxDWbFihaDT6YQPPvhAOHDggDBjxgwhNjZWOHnyZHs/tHb117/+VTAajcL69euFkpIS6U99fb10zCuvvCIYjUbhyy+/FPbu3SvcddddQrdu3YTq6up2fOSRQz49QBB4vkTbt28XtFqt8PLLLwtHjx4Vli1bJsTExAhLly6VjuG5crnvvvuE7t27C999952Ql5cnfPnll0JKSoowc+ZM6ZjOfL5qamqEXbt2Cbt27RIACG+88Yawa9cuabV7MOfmoYceEnr06CGsXbtW2Llzp3D11VcLF198sWC1Wtvr2wqbQOfLYrEIkyZNEnr06CHk5ua6/e5vamqSPkdnOV/NPbc8eU4PEITOc66CwdCqkLffflvo3bu3oNfrhUsvvVQa69SZAfD558MPP5SOsdvtwgsvvCCkp6cLBoNBuOqqq4S9e/e234OOMJ6hlefL5dtvvxWysrIEg8EgDBgwQFi0aJHbx3muXKqrq4XHHntM6NWrlxAVFSX07dtXmDVrlluI6Mzna926dT5/V913332CIAR3bhoaGoRHH31USEpKEqKjo4WJEycKp06daofvJvwCna+8vDy/v/vXrVsnfY7Ocr6ae2558hVaO8u5CoZKEAShLSq6REREREQtxZ5WIiIiIop4DK1EREREFPEYWomIiIgo4jG0EhEREVHEY2glIiIioojH0EpEREREEY+hlYiIiIgiHkMrEREREUU8hlYiIiIiingMrUREREQU8RhaiYiIiCjiMbQSERERUcT7/11IYJfgyLuLAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train(learning_rate=0.0001,batch_size = 1,note=\"SGD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "fd793e82-a941-4770-8aaa-6a9ec232de5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "最终系数为： 2.008732506620374 2.9968403526643916 4.4737372583615445\n",
      "最后迭代次数： 25553\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train(learning_rate=0.0001,batch_size = 2,note=\"2-batch-GD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "1e0a163b-aed8-425b-a6c8-c945da2b26bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "最终系数为： 2.0103233158414575 3.001042617593142 4.315396878649175\n",
      "最后迭代次数： 25251\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZP38+r776KvC/x3mOGjWKY8eOcdNNN/Hbb7+xZ88eFixYwO233+4qQk/P43Q6i2/jRURE5NI4Czj40S0EO4+zk2guu20SHmXgutG/Kltpy7mHH34YNzc3GjZsSGhoKL169WLgwIEMHjyYdu3akZycXKi39FwCAgL47rvvWL9+Pc2bN+fJJ5/k6aefBnBdVxoVFcWvv/5KQUEBPXv2pHHjxjzwwAMEBgbicDjOmmf//v3Ft/EiIiJySXZ/+xy10tZwwnhxpOd7VAuvYneki2aZ0y8uLAPS0tIIDAwkNTWVgICAQsuys7OJi4sjJiam0E09Fd3nn3/ObbfdRmpqKj4+PiXymfpZiIiIFK+jm34i+JvrccMwq+ZTXDfiYbsjuZyvXjtd6b+wUi7JJ598Qq1atahatSobNmxwjTFaUsWoiIiIFK+8tCO4fXsnbhgWeV3NNbc8ZHekS6aCtJxKSEjg6aefJiEhgcjISG688Uaef/55u2OJiIhIUXA6OTBlGLWcx9hlqlH/tvfwdC+7V2KqIC2nHnnkER555BG7Y4iIiEgx2DPr/1ErdTVZxpP4HpPoFFH2rhv9q7JbSouIiIhUQMmbf6bGxokAzKvxMJ0uv9LmRP+cClIRERGRMiI3NRFmnrxu9GfPrvQZNs7uSEVCBamIiIhIWeB0sm/KMEKcyeyhKnVuex8vj/Jx9aUKUhEREZEyYNvXz1A3bRXZxoMjPSZTPTLM7khFRgWpiIiISCl3KHYu9ba8BcBPtR+lQ8eyf93oX6kgFRERESnFThzdh9/3d+OwDD/59qLnzeXjutG/UkFaQdWsWZM33njD9dqyLGbPnm1bHhERETmTyc8hccpggkwa24ih6cj3cS9jz6m/EOVvi+SSxMfH07t37wtqO378eJo3b168gURERIRtnzxAzeytpBo/cgZOI7RyoN2RioUK0jIsNze3yN4rIiICLy+vIns/ERER+WfilnzMZfu/AGBVswk0a9rc3kDFSAVpKdKlSxdGjx7N6NGjCQoKIiQkhH/9618YY4CTp9n//e9/M2LECAIDAxk5ciQAK1as4Morr8THx4fo6Gjuv/9+MjMzXe+bmJhIv3798PHxISYmhs8///yMzz79lP3BgwcZMmQIwcHB+Pn50bp1a1avXs20adN49tln2bBhA5ZlYVkW06ZNK9b9IiIiUtGk7NtI+JKTT1z8Mehmelw33OZExeuiCtIXXniBNm3a4O/vT1hYGAMGDGD79u2F2hhjGD9+PFFRUfj4+NClSxc2b95cqE1OTg5jxoyhSpUq+Pn50b9/fw4ePPjPt+ZcjIHcTHumP4vJC/Xxxx/j7u7O6tWr+c9//sPEiRP58MMPXctfeeUVGjduTGxsLE899RQbN26kZ8+eDBw4kD/++IMvv/yS5cuXM3r0aNc6I0aMYO/evfz888988803vPvuuyQmJp4zQ0ZGBp07d+bw4cPMmTOHDRs28Mgjj+B0Ohk8eDDjxo2jUaNGxMfHEx8fz+DBgy/+ZyIiIiJnVZCVxolPb8KXbH53a8oVd72OZVl2xypWFzWa6tKlSxk1ahRt2rQhPz+fJ598kh49erBlyxb8/PwAePnll3n99deZNm0a9erV49///jfdu3dn+/bt+Pv7AzB27Fi+++47ZsyYQUhICOPGjaNv377Exsbi5uZW9FuZdwImRBX9+16IJw6Dp98FN4+OjmbixIlYlkX9+vXZuHEjEydOdPWGXnXVVTz88MOu9rfeeitDhw5l7NixANStW5f//Oc/dO7cmUmTJrF//35+/PFHVq1aRbt27QCYMmUKl1122TkzTJ8+naNHj7JmzRqCg4MBqFOnjmt5pUqVcHd3JyIi4oK3S0RERC6AMeyacjv18w9wxFTG/5aP8ff1tjtVsbuognTevHmFXk+dOpWwsDBiY2O58sorMcbwxhtv8OSTTzJw4EDgZI9feHg406dP5+677yY1NZUpU6bw6aefcvXVVwPw2WefER0dzaJFi+jZs2cRbVrZ1L59+0K/BXXo0IHXXnuNgoICAFq3bl2ofWxsLLt27Sp0Gt4Yg9PpJC4ujh07duDu7l5ovQYNGhAUFHTODOvXr6dFixauYlRERERKxs7vX6N+0kLyjBtbrniLrjG17I5UIv7R86ZSU1MBXIVLXFwcCQkJ9OjRw9XGy8uLzp07s2LFCu6++25iY2PJy8sr1CYqKorGjRuzYsWK4ilIPXxP9lTawcO3SN/uVE/0KU6nk7vvvpv777//jLbVq1d3XVJxMV39Pj4+/yykiIiIXLT4TUupGTsBgHlVR9Gvez+bE5WcSy5IjTE89NBDXHHFFTRu3BiAhIQEAMLDwwu1DQ8PZ9++fa42np6eVK5c+Yw2p9Y/XU5ODjk5Oa7XaWlpFxfWsi7qtLmdVq1adcbrunXrnvNShpYtW7J58+ZCp9T/6rLLLiM/P5+1a9fStm1bALZv305KSso5MzRt2pQPP/yQY8eOnbWX1NPT09VjKyIiIv/ciePxuM+8HQ8KWO7ViR63PWN3pBJ1yXfZjx49mj/++IMvvvjijGWn98YZY/62h+58bV544QUCAwNdU3R09KXGLvUOHDjAQw89xPbt2/niiy946623eOCBB87Z/tFHH2XlypWMGjWK9evXs3PnTubMmcOYMWMAqF+/Pr169WLkyJGsXr2a2NhY7rzzzvP2gt50001EREQwYMAAfv31V/bs2cPMmTNZuXIlcPJu/7i4ONavX09SUlKhXxZERETk4pj8XA69P5hQk0QcVal75zS8PP7RSewy55IK0jFjxjBnzhwWL15MtWrVXPNP3eRyek9nYmKiq9c0IiKC3Nxcjh8/fs42p3v88cdJTU11TQcOHLiU2GXCrbfeSlZWFm3btmXUqFGMGTOGu+6665ztmzZtytKlS9m5cyedOnWiRYsWPPXUU0RGRrraTJ06lejoaDp37szAgQO56667CAsLO+d7enp6smDBAsLCwujTpw9NmjThxRdfdPXSXn/99fTq1YuuXbsSGhp61l9KRERE5MJsmvYAdbM2kGF8yBjwMeGhVeyOVOIsYy58XCJjDGPGjGHWrFksWbKEunXrnrE8KiqKBx98kEceOTl2Vm5uLmFhYbz00kuum5pCQ0P57LPPGDRoEHDyKUHVqlVj7ty5F3QNaVpaGoGBgaSmphIQEFBoWXZ2NnFxccTExODtXbbuSuvSpQvNmzcv9EjPsqws/yxERERKwvb5H1B/5cnRcxa3eIOu195mc6Kic7567XQX1R88atQopk+fzn//+1/8/f1dPaGBgYH4+PhgWRZjx45lwoQJ1K1bl7p16zJhwgR8fX0ZOnSoq+0dd9zBuHHjCAkJITg4mIcffpgmTZq47roXERERKe8Stq2ixsrHAVgQOoLu/UfYG8hGF1WQTpo0CTjZk/dXU6dOZcSIEQA88sgjZGVlcd9993H8+HHatWvHggULXGOQAkycOBF3d3cGDRpEVlYW3bp1Y9q0acUzBqmIiIhIKZOdmojjq1vwJo/fPNpy5chXy/3g9+dzUafsS4vyesq+vNHPQkRE5EymII+dr/Wg3onf2UckHvcsIaocPmzmYk7Z61n2IiIiIiVo8ycPUe/E72QYb471m1oui9GLpYJUREREpITs/Gkqjfd9AsCqZs/TolUHmxOVDuW2IHU6nXZHqPD0MxAREfmfo7vWEv3LyVGIFoTcQrfr7rA5UelR7kZd9fT0xOFwcPjwYUJDQ/H09KzQFwnbwRhDbm4uR48exeFw4OnpaXckERERW2WlHKVg+lC8yWWNeys6jZyo+uQvyl1B6nA4iImJIT4+nsOHbXp+vQDg6+tL9erVcTjKbUe8iIjI3zIFeex9fwiXOY9wgHAib/8MH2911vxVuStI4WQvafXq1cnPz9cz123i5uaGu7u7fvsTEZEKb8NHD9D8xFpOGC+O959K06gouyOVOuWyIAWwLAsPDw88PDzsjiIiIiIV1Kbv36H5oc8BiG0xgU6tLrc5Uemkc6kiIiIixWDf+p+pt+ZpABZH3E6nAXfanKj0UkEqIiIiUsRS4vfgP3sEnlY+q72v4Io7X7E7UqmmglRERESkCOVlpXN8yg0Ek8pOR03q3f0ZHu7l9irJIqGCVERERKSoGMO294YRk7+bZBOA29AZVK5c2e5UpZ4KUhEREZEisv7zJ2iSsphc48aeqyZTq85ldkcqE1SQioiIiBSB7Ys/p/mudwH4tcETtOl8jc2Jyg4VpCIiIiL/0KFtv1F96YMALKl8PV2GjLM5UdmigvQCFRzZancEERERKYXSjh7G/cuh+JDDOo8WtL9nkh4Mc5FUkF6AIwvfhEkdObTgLbujiIiISCmSm32Cwx/cQLg5yn4rkmp3zcDby8vuWGWOCtILsHLrftxwEr7iaZLX/2B3HBERESkFjNPJ5km30iB3M2nGl7wbpxMaGmF3rDJJBekFuGrkC8z36IY7Trxn38GJgxvtjiQiIiI2i/3kMVqkLiTPuLGn6yRqN2xpd6QySwXpBQjw8aTR3R8RSyP8yOLE1IHkp8bbHUtERERssmHuB7Te+x4AvzV8guZdBtgbqIxTQXqBqlUJwvOW6ew1EVQpSCThvYGQl2V3LBERESlhu9cu4rLVjwGwPGwoHQfpjvp/SgXpRWhSpyb7ek7juKlEtRNbiPtwGDiddscSERGREpK4bxvB39+Gp5VPrM/ltL/rLd1RXwRUkF6kzh07sKzlRHKNGzFHFhL39eN2RxIREZESkJmaTPbHN1CZNHY6alP33um46xn1RUIF6SXo3/9GZlc/2VUfs3UyBxd/aHMiERERKU4Febnsm3QD1Z0HOEIwviO+ISAgyO5Y5YYK0ktgWRbXjXiY/wbcBED40kdJ3rTI5lQiIiJSHIzTybr37qRh9u9kGi+S+39K1eq17I5VrqggvUQebg663vsmS9yvwIN8PGcO58ThbXbHEhERkSK2+ov/R+uk/+I0Fps7TKRhyyvsjlTuqCD9BwJ8vKhz1ydspC7+JoP0jwaSn5ZodywREREpIr/Pm0bbHRMBWFX3Idr2utnmROWTCtJ/qFpYCNw0nYOmCuH5hzg8eQAmN9PuWCIiIvIPbVu9gIYrH8ZhGVZXGUiHof+yO1K5pYK0CDSpX4+4np+QYvyofmIzce8NBWeB3bFERETkEu3fsZ6IH2/D28pjnW9HWt/zAZZDZVNx0Z4tIp06Xs7Ktm+TY9yplbyEXZ+MBmPsjiUiIiIXKSnhAO5fDCKIDHa416PBqK9w0/BOxUoFaRHqfc1A5tYdD0CdvdPZM+dFewOJiIjIRTmRkcrxD68jyhzhkBVOyMhZ+Pj52x2r3FNBWsSuHTqa2aH3AlBr3Ysc+OVTmxOJiIjIhcjPy2XnO4Oom7+T4/jjHPo1IeHV7I5VIaggLWIOh0Xvu/7Nj34DAAj/aSyJm36yN5SIiIicl3E6iZ08kmZZq8g2HhzpM5Xous3sjlVhqCAtBl4e7lw+6j1+9eiAJ/n4fDOMtP0b7Y4lIiIi57D6s6dplzwbp7HY0uE1GrTtbnekCkUFaTEJ8PWm1j3T2WjVx59McqYNJPvYIbtjiYiIyGlW/3cy7fe8BcBv9R+mZa/hNieqeFSQFqPIkGB8bv2avUQS6kwk8b3+OLPS7I4lIiIif1q3dDYtfn8CgNXhQ2ivsUZtcdEF6bJly+jXrx9RUVFYlsXs2bMLLR8xYgSWZRWa2rdvX6hNTk4OY8aMoUqVKvj5+dG/f38OHjz4jzaktKoTU4PkAZ+TbAKonrOLuHevw+Tn2B1LRESkwtvy+y/U/fkePK0C1vt3ps1d79odqcK66II0MzOTZs2a8fbbb5+zTa9evYiPj3dNc+fOLbR87NixzJo1ixkzZrB8+XIyMjLo27cvBQXlczD5Vs1bsbnrh2QaL2qnr2Xn5JvB6bQ7loiISIW1d8cfhM+5mUpWFlu9mtFo9Awcbm52x6qwLnqU1969e9O7d+/ztvHy8iIiIuKsy1JTU5kyZQqffvopV199NQCfffYZ0dHRLFq0iJ49e15spDLhyi49WZA2kS6xY6iXtJBt0+6jwW2TwLLsjiYiIlKhJBzah/v0GwghlTi3WtQYNRsPL1+7Y1VoxXIN6ZIlSwgLC6NevXqMHDmSxMRE17LY2Fjy8vLo0aOHa15UVBSNGzdmxYoVZ32/nJwc0tLSCk1lUY/+N7Ow3nicxqLB/i/Y/vUzdkcSERGpUFKOJ5Ex5VqqcYTDVgSV75qDb0Cw3bEqvCIvSHv37s3nn3/Ozz//zGuvvcaaNWu46qqryMk5ed1kQkICnp6eVK5cudB64eHhJCQknPU9X3jhBQIDA11TdHR0UccuMX2GjuGHqg8AUH/Lm+yc+5bNiURERCqGrBOZHHj3Ouo44zhGII7hswkKL7s1RXlS5AXp4MGDueaaa2jcuDH9+vXjxx9/ZMeOHfzwww/nXc8Yg3WO09ePP/44qamprunAgQNFHbvEWJZFnzvH82PlmwGotfop9v7yhc2pREREyre8vDw2vz2IJnl/kIEP6Td8SUTNy+yOJX8q9mGfIiMjqVGjBjt37gQgIiKC3Nxcjh8/XqhdYmIi4eHhZ30PLy8vAgICCk1lmZvD4qr7/sPPfr1xswxRP43m0LoFdscSEREpl4zTyZp3b6f1ieXkGncO9ZpCjcYd7I4lf1HsBWlycjIHDhwgMjISgFatWuHh4cHChQtdbeLj49m0aRMdO3Ys7jilhpeHO21Hf8xKz5NPcwr6760c3fmb3bFERETKFWMMv3wwjo7H5+A0Ftsun0j99tfYHUtOc9EFaUZGBuvXr2f9+vUAxMXFsX79evbv309GRgYPP/wwK1euZO/evSxZsoR+/fpRpUoVrrvuOgACAwO54447GDduHD/99BPr1q3jlltuoUmTJq677iuKSj5e1LvvS9Y7GuNHFm7TbyT14Ha7Y4mIiJQbiz+bwJXxHwGwrulTNO1xq82J5GwuuiBdu3YtLVq0oEWLFgA89NBDtGjRgqeffho3Nzc2btzItddeS7169Rg+fDj16tVj5cqV+Pv7u95j4sSJDBgwgEGDBnH55Zfj6+vLd999h1sFHP8rJCiQ0LtmssOqSbBJIeuj/mQmld1rZEVEREqLJV+/TZddrwDwe617aXX9OJsTyblYxhhjd4iLlZaWRmBgIKmpqWX+etJTdsftxvPj3kRzhIPu1aky5ie8A8PsjiUiIlImLf/uY9qvHYu75WRD5CCa3fW+xv4uYRdTr+lZ9qVE7ZjaZAz6hgQTTLX8/SS8cw25Gcf/fkUREREpZNWimbRZ+9DJYjSkD01HTlYxWsqpIC1FLmvYlCMDvuSY8adm7g72v92P/OwMu2OJiIiUGb//Op+mv9yLl5XPxsDONL3vEyxHxbsksKxRQVrKNGvRlrjen5FmfKmTvZFdb1+HMzfb7lgiIiKl3qbY5dRecBu+Vg5bfNvQcNRXWG4edseSC6CCtBRq1b4LW7p+yAnjRYOM39j67mBMQZ7dsUREREqt7Zt+J3LOTQRamezwakzd+2fj5ultdyy5QCpIS6n2Xa7h945vk2PcaZSyhE2ThoPTaXcsERGRUidu11YCv7mBECuNPe51qD76ezy8K9kdSy6CCtJS7Iqeg1jV6lXyjYMmST/wx4f3QNkbFEFERKTY7N8Xh9tnA4ggmQNu0YTd9wPe/pXtjiUXSQVpKde5/20sa/QsAE0Pf8mGTzSGmoiICMDBQ4fIm9af6iQQ7wjHf+QPVAqOsDuWXAIVpGXAVYPuZ1GtRwFoFjeFP6b/y+ZEIiIi9jqUEE/Gh32pbfaTZAXjdft3BEXUsDuWXCIVpGVEt2GP81PVUQA03fEWG7581uZEIiIi9khIPELq+/1oYPZw3ArEunU2wdXq2x1L/gEVpGWEZVlcdefz/Bw5EoBmW19nw1fP25xKRESkZB1NSiJpcj8aOneSgj8Ft8wmJKaZ3bHkH1JBWoZYlkXXu17h5/DbAGi25WU2zHzZ5lQiIiIl4+ixY8RP6kdj53bSqETu0FlUqd3S7lhSBFSQljGWZdHlrtdZHDoMgGYbn2fD7Ik2pxIRESlex1JSOPTOtTQt2EI6vpwY8g1h9drYHUuKiArSMsjh5qDzPf9haZUhADRbP54/5rxlcyoREZHikZKWxt63B9C84A8y8CH9hq+IaNDB7lhShFSQllEONwed7p3EsuAbAGgc+xR/fP+uzalERESKVmp6Brveuo6W+es4gTcp131BVONOdseSIqaCtAxzuDm4fNQHLK98HQ7L0HjNE/zx4wd2xxIRESkSKekZbPvPdbTOW0sWniRf+ynVmnW1O5YUAxWkZZybm4MOo6fwa1A/HJah0ar/Y+O8j+yOJSIi8o8cT8tg839uoF3eb2TjydG+HxPdoofdsaSYqCAtB9zc3Gg3ehorAnrjZhkuWzmODT9+aHcsERGRS5Kcksa2/wzk8ryV5OJO0jUfUb11H7tjSTFSQVpOuLu703bMp6wK6IW75aTxqodZ//1ku2OJiIhclKSUVHa9fR0d8leTgwdJfadRrU0/u2NJMVNBWo64e3jQ+v7PWRl0DW6Woemax/h99n/sjiUiInJBEo8dJ+6ta2mXv5ZsPEnu/wlRrVWMVgQqSMuZUz2lKyoPwGEZWq5/ithvX7c7loiIyHklJh/jwDvX0qZgHVl4cXzAdKJa6jR9RaGCtBxyc3Oj/eiprKhyckioVn88y5qv9UQnEREpnY4kJXPo3f60KtjACbxJHTiDyObd7Y4lJUgFaTnlcHPQ4b4PWBF2cvD8Npuf57cZz9ucSkREpLD4xKMkvNuXFgUbycSH9Bu/IqLpVXbHkhKmgrQcsxwOOtwziV8jTj5mtO22l1n92Xh7Q4mIiPxpf3wCRyf3pZlzCxn4kjHoG8IbdbY7lthABWk5ZzkcdLzrP6yoejsA7XZNZNXH/7I5lYiIVHS79x8k9f2+NHVuIx0/Ttz0LeENr7A7lthEBWkFYDkcdLjzdVZWvwuA9nFvsfLDcRin0+ZkIiJSEW3dtYe8j66hidlJmuVP3i2zCauvZ9NXZCpIKwjLsuhw+yusjBkNQIeDH7J60t04CwpsTiYiIhXJhs2b8fq0Lw3YS4oVBLd+R3CdtnbHEpupIK1gOgx/nt8aPAZA+6Nfseatm8nPy7M5lYiIVARrf48l5KtrqWUdIskRivvIeQTEtLA7lpQCKkgroLZDHmdtiwkUGIt2KT+y4Y2BZGdn2R1LRETKsV9X/EL0f6+nmnWUBPcoKt37E5WiLrM7lpQSKkgrqNbXjmLT5f8h17jRKnMZ2yf2JTMjze5YIiJSDi1ZsoDL5g8h3DrOQc9aVB79E96hNeyOJaWICtIKrFmPW9nZbQpZxpNmOWvZ+2YvUo4n2x1LRETKkQU/fkurxbcSbGWwz/syIu5fhFdQlN2xpJRRQVrBNbryOg70nU46PjTK20zi2z04euSQ3bFERKSMM8bw368/ptOqu/G3sthTqQXRDyzAvVKI3dGkFFJBKtRr053kG2ZxnADqFewiY3JPDu3fY3csEREpo5xOw1cf/4femx7Ex8pld+XLibl/Lg6fALujSSmlglQAqNm4Aydu/o5EK4QYcwDro57s3rre7lgiIlLG5OQX8M3kp7kx7hk8rQLiwntQe9RsLE9fu6NJKaaCVFyq1m2Odds8DjkiiSKRyl/2ZeNvP9sdS0REyoiM7Dx+fHM0gxL/g8MyxNUaSszdM8Dd0+5oUspddEG6bNky+vXrR1RUFJZlMXv27ELLjTGMHz+eqKgofHx86NKlC5s3by7UJicnhzFjxlClShX8/Pzo378/Bw8e/EcbIkUjtHo9/O/9md3udQkmnVo/DGHNwq/sjiUiIqVcclomv068mQHp0wHY22QsMcPeBYebzcmkLLjogjQzM5NmzZrx9ttvn3X5yy+/zOuvv87bb7/NmjVriIiIoHv37qSnp7vajB07llmzZjFjxgyWL19ORkYGffv2pUBPDSoVAkKjqDp2EVt8WuFn5dB8+T0sn/mO3bFERKSUOpB4jK1vXkfPnPkUYHHg8gnUvP5ZsCy7o0kZYRljzCWvbFnMmjWLAQMGACd7R6Oiohg7diyPPvoocLI3NDw8nJdeeom7776b1NRUQkND+fTTTxk8eDAAhw8fJjo6mrlz59KzZ8+//dy0tDQCAwNJTU0lIEAXSBeXgrwcNr0zlGYpiwBYXOMBuox4Fkv/wYiIyJ927DtAxrRBtDRbyMWd5J6TiOwwyO5YUgpcTL1WpNeQxsXFkZCQQI8ePVzzvLy86Ny5MytWrAAgNjaWvLy8Qm2ioqJo3Lixq83pcnJySEtLKzRJ8XPz8KLp/V+xLuomALrue5Ol79xLfn6+zclERKQ0+O2PLZiPrqGl2UImvqTf8KWKUbkkRVqQJiQkABAeHl5ofnh4uGtZQkICnp6eVK5c+ZxtTvfCCy8QGBjomqKjo4sytpyH5XCjxchJrK//IABdkr7gt4mDycrKtjmZiIjYaf7SX4ic2Z/61j5SHJVxDv+ekMZX2x1Lyqhiucv+9FO6xpi/Pc17vjaPP/44qamprunAgQNFllUugGXR/KbxbGr7IvnGQcfMRWx9vQ9JSUl2JxMRkRJmjGHmt1/R7ufBRFtHOeoRhc89P+Ef08ruaFKGFWlBGhERAXBGT2diYqKr1zQiIoLc3FyOHz9+zjan8/LyIiAgoNAkJa9xn3uJu/oDsvCiZV4sKe90I27PdrtjiYhICckrcPLFRxPpu+FegqxMDvk1IuT+ZXiF1bY7mpRxRVqQxsTEEBERwcKFC13zcnNzWbp0KR07dgSgVatWeHh4FGoTHx/Ppk2bXG2k9Krb6QaSb5xFshVEHbMX3096sX7NL3bHEhGRYpaRnce3bz3M0APP4mXlsy/sKqo+sAiHf6jd0aQccL/YFTIyMti1a5frdVxcHOvXryc4OJjq1aszduxYJkyYQN26dalbty4TJkzA19eXoUOHAhAYGMgdd9zBuHHjCAkJITg4mIcffpgmTZpw9dW69qQsqNboclIq/8SBKQOILjiA3/c38EvSm3TqPcTuaCIiUgyOpGQQ++4dDM6dB8C+usOpcdNEjTEqReaiC9K1a9fStWtX1+uHHnoIgOHDhzNt2jQeeeQRsrKyuO+++zh+/Djt2rVjwYIF+Pv7u9aZOHEi7u7uDBo0iKysLLp168a0adNwc9OBXVYERdXBe+wytr87kPpZ6+iw6l4WJO2n+y3/p2GhRETKkR0HEkiaOpQ+zlicWBxu9zQ1ej9kdywpZ/7ROKR20TikpYczL4ct7w2ncdKPACwMuYUr73kDLw8Pm5OJiMg/tXzdRirPHkYjK44cPEnrM4nQtjfYHUvKCNvGIZWKx+HhReNRX7Cxzr0AdE/+jDWv3UCKxooVESmzjDF8++N8YmYPoJEVR5ojkJyb/6tiVIqNClL55yyLJre8yPb2L5Nn3LgiewkH3uhB3N69dicTEZGLlFfg5JOPJ9Nz1TCqWkkc9ayG9z2LCairG4+l+KgglSJTv9fdxPf7jDT8aOLciue0q1mzapndsURE5AKlZuby1Zv/x7C4x/GzcjhcuQ1Vxv6Cp4Z1kmKmglSKVPXWfSi4fSGH3apSlaM0/PEGFs6aShm8VFlEpEKJO3KcFROHcHPahzgsw8FaQ4ga/SOWb7Dd0aQCUEEqRa5y9UaEjP2FnX6t8LNy6Lb+Qea99xi5eQV2RxMRkbP4bfMOjk3qTe/8nyjAQcLlz1Ft2GRw0w2qUjJUkEqx8PIPoc6D89hSdRAOy9A7YTIrXxtEcopudhIRKS2MMcxZ+BMRX11DK7aSafmSPnA6Ed0fAA3hJyVIBakUG8vdk4YjP2BH6/HkGwedsxdx+M2r2blnt93RREQqvJz8AqZO+4Auy2+mupVIkkcU7iMXEdS0t93RpAJSQSrFrl7fBznS/3PS8aOJ2Y7fxz34dfliu2OJiFRYR1Kz+HLiOIbvfYQAK4vDQS0JGfsLXlGN7I4mFZQKUikRVVv1wdz5E4fdqxFlJdFy4SC+/+xNCpy62UlEpCSt23WQP964jlszp+JmGeJrDyJq9Hwsvyp2R5MKTAWplJiAapcRNvYXdgZ0wMfKpe+up1k48Q5SMk7YHU1EpEL4fvGv+Hzai+5mJXm4k9z1JSKHfQDunnZHkwpOBamUKPdKwdQd+wPb690NQK/0mex5vTvbd8fZnExEpPzKzXcy7ZMPuWLJjTSwDpDqFkz+sDmEdL7H7mgigApSsYPDjfpDX+ZA9/c5gTctnZvw/6QbixcvsDuZiEi5k5iaxVdvPMSw3Q8TZGWS4N+YgPuX41P7crujibioIBXbRF8+mPzbFxHvXo0oK5mOS4Yye9or5BU47Y4mIlIurN62nw1vXMctGSevFz1c60YiHvgZK7Cq3dFEClFBKrYKqN6EsId+ZVflTnhZeQzY+28WvTacRI1XKiJyyZxOw/S5iwia3sd1vejRzi8QNewDcPeyO57IGVSQiu3cfIOoM2YOuxqOAaD3iTnEv3E1a//4w+ZkIiJlT+qJPN6f9Cr9V99MfccB0tyCcQ6bQ2jX+zTYvZRaKkildHA4qDPo3xzuM5V0/GjGdmrN7M2cr6fh1NBQIiIXZPP+oyx8fTj3HP03laxsjgS3xv+BFXjpelEp5VSQSqkS1XYgHvct54B3fYKtDPpvfoDv3riX5LRMu6OJiJRaxhj+u3Q1eVN6cUP+DwAcbT6K8FHzsQIibU4n8vdUkEqp4x1Wi+iHf2FXjSEAXJv2BXsn9mDdlu02JxMRKX1O5Obz4Ufvc+XPA2lu7SLT4U/mwM8JHTAB3NztjidyQVSQSunk7kWd297j8NXvkIU3rcwmqn3ZnTmzv9QpfBGRP20+eIyZr97LyAOPUNnKING/IT6jl+PXtK/d0UQuigpSKdWirrgFc9diDnvFEGqlcs26u5n9nwc5lpFtdzQREdsYY/j659Wkvd+XYblfAZBQ/xbCHliCI7imveFELoEKUin1fKMaEjnuV/ZU7Y+bZRiYMpVdr13Nmj822x1NRKTEpZzI5e3Jb9Ft6UA6ODaTbXmT0fc9Im56R0M6SZmlglTKBMvTj1ojP+XQla+QhRdtzUZqzezJ19M/JDdfA+mLSMWwZlc8818bwZgjTxFsZZDs3wCvUcup1HqI3dFE/hEVpFKmVL3qLrhrCYe96xJipXPjjnHMe3U4exOS7Y4mIlJsCpyGT+YsxO+TngwuOHkXfVKTkYQ8sAyrSl2b04n8cypIpczxiWpI1MO/srfOcAD6Z88he1JX5i9ZijG64UlEypeDxzL54M3x3BB7Mw0d+0h3CyL7xhlUuf5VnaKXcsMyZfAbPC0tjcDAQFJTUwkICLA7jtjo2PrvcJszikBnKlnGk9kR99Nn+KME+nraHU1E5B8xxvDdb9vwmPsQva0VACRWaU/Y8I/BP8LmdCJ/72LqNfWQSpkW3LwflR5Yzf7K7fCxcrnpyKvEvtqftVt22R1NROSSHc/M5c0Pp9Bybl96WyvIx43jHZ8g7L4fVYxKuaQeUikfnE4O/fgKYWtexoN8jpggfqr3NAMHjcDbw83udCIiF2zZ1oMc/PpRhjq/ByDVuyp+N03FvUY7m5OJXJyLqddUkEq5cmLvWtK/uJ3wnH0AfOfRk5ihE2kcU9XmZCIi55eVW8C0mbPptvUp6jkOAZDcYCgh170CXpVsTidy8XTKXios35qtCX94NQfq3wZAv7z5+E/rwoyZX5NXoOGhRKR02rAviemvjuHObSOp5zhEhnswuYNmEDJkkopRqRDUQyrlVvrWn8mbeQ/B+UdwGouZPtfT/NaXqBtVxe5oIiIAZOcV8PEPP9Pm98dp6dgJQFJ0T6oMmQR+ITanE/lndMpe5JTsVPZPf4Dq+2cBsM1UZ2PblxnYuxduDsvmcCJSkf2+L5nlX7zEnVnT8LVyyHL44ez9Mn6tbwZL/z9J2aeCVOQ0Kb9/i+P7BwlwppBr3JjpO5gWt/w/GlRVb6mIlKzsvAI+mrOIVhuepp1jGwDJoe0IuXkKBEXbnE6k6KggFTkLk5HIoU/vptqRnwHY7oxmbfP/xw39++PlrjvxRaT4rdlzlDUzJnBbzmf4WLnkWD4UdHsG3453g0O3dUj5ooJU5FyMIWXtlzh+fJQAZwoFxuJbr2upM+QFWtSKsjudiJRTJ3LzmTp7Hh03PUMLx8lxko+FdyR4yGSoXMPmdCLFw9a77MePH49lWYWmiIj/DeJrjGH8+PFERUXh4+NDly5d2Lx5c1HHEDk7yyKozRD8x8VyKLofbpbhxtzZBE3rwrTpn5GZk293QhEpZ5ZsPcSnL9/PnZuH08KxiyyHHyd6vUHwPXNVjIr8qVjODzRq1Ij4+HjXtHHjRteyl19+mddff523336bNWvWEBERQffu3UlPTy+OKCJnZflVoeodn5E+8HNS3EOJcRxhxI5RLHh5KL9u3mN3PBEpBxLTsnn5o+mEftGbu/M/x8vKJzmqCz4PrMG3/W26cUnkL4qlIHV3dyciIsI1hYaGAid7R9944w2efPJJBg4cSOPGjfn44485ceIE06dPL44oIufl37QvQQ/HcrjOTQBcVzCfWl9148P33yAxNcvmdCJSFjmdhi+Xb2bR68N5eN99NHLsI8vNn+x+kwgZORsC9aAOkdMVS0G6c+dOoqKiiImJYciQIezZc7LHKS4ujoSEBHr06OFq6+XlRefOnVmxYsU53y8nJ4e0tLRCk0iR8Q4k6pbJZA39L8e8qhJpHePOw8+w7fXefLNoOQXOMneZtYjYZFt8Kq++8TKdF17DUObhsAzH6wzE58F1eLcaql5RkXMo8oK0Xbt2fPLJJ8yfP58PPviAhIQEOnbsSHJyMgkJCQCEh4cXWic8PNy17GxeeOEFAgMDXVN0tIbFkKLnU68LwQ/HktjiAfJw50prHdf8ch2fvXo/f+xNtDueiJRimTn5TJr9M4cnXcsjaROIsI6T5hNNwS3/pfItU6FSqN0RRUq1Yr/LPjMzk9q1a/PII4/Qvn17Lr/8cg4fPkxkZKSrzciRIzlw4ADz5s0763vk5OSQk5Pjep2WlkZ0dLTuspdiU5C4naMzRhFxbA0AO51VWVrvMW68/iYCfTxsTicipYUxhh/W7yfu+1e5I/9LfK0c8nEnq939+F/9KHh42x1RxDal6ln2fn5+NGnShJ07d7rutj+9NzQxMfGMXtO/8vLyIiAgoNAkUpzcwuoTMWYhab3fId0tiLqOQ9y5awzLXr6B/y5fh1On8UUqvG0JaUx4610azOrFmIJP8LVyOB7aBvdRK/Hv/YyKUZGLUOwFaU5ODlu3biUyMpKYmBgiIiJYuHCha3lubi5Lly6lY8eOxR1F5OJYFgHtbsH/4fUk1D1501M/s4SuC3sz9dVx/L7n3JeZiEj5lZqVxxtfL2LfuwN58tgT1HEc5oRHZfL6vk3l+xZCaD27I4qUOe5F/YYPP/ww/fr1o3r16iQmJvLvf/+btLQ0hg8fjmVZjB07lgkTJlC3bl3q1q3LhAkT8PX1ZejQoUUdRaRo+FQm4ubJ5O29jZSZDxCavpU7Tkxh97S5TKo+lgE3Dicy0MfulCJSzJxOw6w1u0ia9xL3OGfj7cijAAcnmt+Of8+nwCfI7ogiZVaRF6QHDx7kpptuIikpidDQUNq3b8+qVauoUePk4L+PPPIIWVlZ3HfffRw/fpx27dqxYMEC/P39izqKSJHyqNmO0AdXkL5qGtZPz1KbeO49+CiLX/+ShW2eYlDPznh76BGkIuXRyl1J/Dx7CsPT36ealQQWpIS3J2jgRPzDG9odT6TM06NDRS5FVgpJP/w/gjZNxZ0Ccow7X3v0I6T3k/RqWQdLQ7uIlAt7jmbw+ew5dNv/Fh3dtgCQ4RWB1zUv4NHkOg3jJHIeepa9SAkxidtI/GYc4YnLAThqAvim0i20vO4B2tWJ+Ju1RaS0OpaZy7QflxOz4XWuc/sFgDzLk7x2o/C96v/A08/mhCKlnwpSkZJkDDlbfuDEd49TOXs/ALudkcyNuIeeA2+nXoSOUZGyIie/gOnLNpG3bCK3mu/xtvIASK97Hf7XPAdB1W1OKFJ2qCAVsUNBHum/foBj6Uv4FaQA8JuzAWvqjuWGa68jPEBDwIiUVvkFTmbH7iNuwSRG5H1BqHXyiYCpYW0IvPYlqNrK5oQiZY8KUhE7ZadxfOHL+P3+Hp4mF4C5zvYcavV/DOremUBfDawvUloYY5i38TC/zZ3GzSc+o47jMADpfjXwveZ53C7rq+tERS6RClKR0iD1EEnfPUPwrm9wYMgzbsy2upLediw3XtUef28VpiJ2Mcbwy46j/Pz9dG5InUpjx14Asj2CcOv6GB7t7gQ3/RsV+SdUkIqUIiZhI0mzHyc04eSNETnGnZlWd3I7PMigrq3w9Szy0ddE5Dxi9x3nuzlf0+foh7R1bAcgx80P2t+HV6f7wVvfKyJFQQWpSCnk3LuCY98/TZWkNQBkGU++cvTGrdOD3NCpqcYwFSlma/YeY86PP3D14ffp7PYH8Oed863uxLfrw+AXYnNCkfJFBalIaWUMBbuXkPL904SknPxCTDc+fOnWF69OY7j+8kbqMRUpYit3J/PDj9/R9cg0urmtA6AAN7Ka3Eyl7o9DQJTNCUXKJxWkIqWdMeRvn0f63PFUTtsGnCxMv3b0wrS7lxs6tyTQR9eviVwqYwwrdicz78dZdE/8mCvdNgLgxEFWg4H49fgXBMfYnFKkfFNBKlJWOJ3kbZ5N5oIJBKXvBE6eyv+Gq8lodQ+DrmpPSCUvm0OKlB1Op+HnrUf4ZdG39Er6lA5/Pl2pADeyG96AX7dHIaS2zSlFKgYVpCJljdNJwba5pC54keCUkz05Ocad2aYzCU3v4carOxEV5GNzSJHSKye/gP/+fpANi79mQOaXtHHsAKDAcien0RB8r3pYPaIiJUwFqUhZZQzOXYtJWfACwUd/AyDfOJjrbM/2WsPp2b0XTasF2ZtRpBRJzcrji5U7OfrrpwzJ+y91HYcAyLc8yW16C75dH4KgaJtTilRMKkhFygGzbwXH571AcPwy17xVzstYGjyIFlcPoVvDSNwcGrBbKqZDKVl8sWQDbr9P5WZrHmFWCgC5bn7QajieV9wPAZH2hhSp4FSQipQn8RtI+Wki/rvm4EYBALudkfzX+1rCrxzBdW3r6s58qRCMMazck8wPS1dTe8+nDHb7GT8rB4AT3uF4Xj4K9zYjwDvQ3qAiAqggFSmfUg+R8cu7uK+bhndBBgDHTCW+sXqQ2WQY/Tq1pU5YJZtDihS9E7n5zPr9IBt/mcNVabPp5vgdN+vkV1dGYH38uo7FanwDuHvanFRE/koFqUh5lpNOzppPyP31bfyzTj53u8BYLHS25vewgTTvPIDujSLwcHPYHFTkn9mXnMmXy7eQv246g5zzXM+ZB8is1gm/LmOhdjc9a16klFJBKlIRFOTj3Po9acveJShxtWv2bmcks9174d1mGAM7NiQyUHfnS9mRnVfAgi1H+GXFchof+orr3X6hkpUNQK6bL6bZULw63AWh9W1OKiJ/RwWpSEWTuJWMX9/DY9NXeBVkAnDCeDHH2ZGdVa+jVcfudGsYjpe7Hk8qpdOOI+nMXLmDrA3f0K9gkWvYJoDMgFr4XH4vjmZD9Jx5kTJEBalIRZWTTv76GZxYPpmA9F2u2TucVfne7SoKGg+mT4emNIrSTR9iv/TsPH78I561KxfR/Ogc+rmtwt/KAsCJG9m1uuN7xb0Q01mn5UXKIBWkIhWdMbBvBekrPsR71w94OE/eiZxn3FjsbM7KgD7UaN+ffi1q6ElQUqLyCpws23GUhWs2EbBzNgOtxTRwHHAtP1GpOt5tR+BoPlTDNomUcSpIReR/slNxbvyW9FVTCUze4Jp91ATyvbMD+6L60Kh1V3o2iSTA28PGoFJeGWP4fX8KP8buJGvjHK7OX0Ynx0bcLScA+Q4v8uv3w7vdbVDjcvWGipQTKkhF5OwSt5G95hPMhi/wyT3mmr3PGcZc05GEGv1o07Yj3RqE4+Op603l0hlj2Hw4jQV/HOTI+rl0PPEz3R2x+P45bijAiSpN8Wl7K1aTG8EnyL6wIlIsVJCKyPkV5MGuRWSsnYHX7nl4OLNdi7Y6o5nH5aTU6kfrFi3pUj8Uf/WcygVwOg3rD6aw4I+DJG5cSKvM5fR2W02wleFqc6JSDbxbDsHRdBBUqWNjWhEpbipIReTC5WZitv9IRuwMfPctxs3kuxZtdVZnoWnD0apX06B5R7o3jCAswNvGsFLa5BU4id13nEV/7CNt03za5fzK1Y5YAq0TrjbZXiG4Nbkej+ZDoGpLnZIXqSBUkIrIpck6jtkyh4y1X+IXvwrHn48qBTjgDGWBszVxVbpQtVlXOteP5LJIfywVFxVOUkYOS7YfZfWWXVi7f+LKgtV0dax3PcYTIMcrBMdlffFofO3Ju+Td9HhbkYpGBamI/HMnjsGO+WRsmI3XvsWuO/Xh5CNLlzmbss6zFdTuRsuG9ehUN5RgPz26sTwqcBo2H07l560J7Nu8mqpJy+niWE8La6frEZ4A2b6RuDfqj3vjARDdDhy6DlmkIlNBKiJFK/cE7P6ZrI1zcOych1deaqHFG501WeZsxsGQjoRd1ol2dcNpWb0y3h4qSMoiYwy7EjNYsTuZDTt249i7nLb5sXRx20CYlVKobVZQPbwaXYOjYX+IaqHT8SLiooJURIpPQT4cWE3+zkVkb51PpWObCy1OMz785mzAWhqSEtaG0LptaVs7jFY1KuPrqdO2pZExhr3JJ/gtLpl1O/aSt+dXGuZsoINjCw2s/Tj+0gua5+ZDQc3OeF/WE+p0h6BoG5OLSGmmglRESk5G4sne063zcez+Ga+8lEKL040Pa531WGMakhzahsq129K0RhWaRQcRFeita1BtkJVbwIaDKcTuO87OuDg4uJbLcjfSwbGFRtbeQqfhAbKC6uLVoAeOej2gegdw18MUROTvqSAVEXs4CyB+A2bvcrJ2LsP94Co889MLNckynmwyNVnvrMMezwY4o1oRHVOPZtUr07RaEIE+GmKqKOXkF7DzSAabD6ey9dAxjsdtIDB5Hc2tnbSwdhLjOHLGOlkBMXjW6YxbrSuhZieoFGZDchEp61SQikjp4CyAI5tg76+c2LkU9wMr8MxLO6PZURPAemcdNjhrk+hbFxPeiLBqtWkQGchlkf7UDPHD3c1hwwaULckZOexMzGBbfBrbDiaReXATlY5voQFxNHLso6G1r9DA9KdkBdXBs2aHPwvQKyAgyob0IlLeqCAVkdLJ6YRju+HgWvIPrCFn3xp8krfg+MvYp6ekGl+2mepsdVZnl1WDE5Xr4xlWj/DwSGKq+BFTxY+aVfwqXI9qfoGT+NRs4pIy2ZWYwe7EVNIO78bt2A7Cc/ZR13GIRtZe6liH8LAKzlg/z8OfgshWeMe0h2ptoFor8Klsw5aISHmnglREyo68bEj4Aw6uJffA7+THb8Q7ZddZi1SAZONPnIlkjzOSOBPJUa9qOINi8AiuTlBwFapW9iUq0IfIIG+qBvkQ6ONRpq5TPZGbz5G0HBLTsklIy+bg8SwOJqeTeXQ/JmUfPpkHqUoita14aluHqGUl4GXlnfW9cj0CcYY3wSu6OVZkM4hoClXqgUO9zSJS/FSQikjZlp8LSTvgyCZMwiayD27AStqOd9aZ1zv+Vbrx4bAJ4ZCpwiFThcOmCsfdKpPnFUKBXyiWXxgegeFUruRLSCVPgnw8qeTtTiUvd/y83PH/y9+9PRx4OBw4HBdXzBpjyC1wkp3rJDu/gKzcArLyCsjIySflRB6pWXmknMj98888MjMzyE89jEk/gvuJRALykwmzjhNGClFWMtFWIpHWsbP2dp5S4PAiN6g2HhENcA+rD+GNIbIpBEZrGCYRsU2ZKUjfffddXnnlFeLj42nUqBFvvPEGnTp1+tv1VJCKVFA5GSdP+SfvgqRd5B3dQd6RHbilHcAr9/gFv02K8SPZBJCOL2nGl3R8yPjzz3TjSybe5OJOHu7kWx44HZ4UODwxDg8shwMLgzGAcZ58Q+PEGCduzjzcCrLxIhfvU5OViw+5BJBJoPXnxP/+PNs1nWfjtNzJrVQNK7gGniExWCG1IbT+yR7PoOoahF5ESp2LqddsGxTwyy+/ZOzYsbz77rtcfvnlvPfee/Tu3ZstW7ZQvXp1u2KJSGnmVQkim52cAI8/JwByMyH1EKTuh9SDkHKAgpQD5KYmQMZRHCeS8MhJxmEKCLIyCbIyL/7znX9O5+L4c7pIBQ4v8nzDMJXC8QiMxD0wEiqFQ0BVqFwDgmrg8I/EW6faRaScsq2HtF27drRs2ZJJkya55l122WUMGDCAF1544bzrqodURC6J0wlZxyHz6MkpJx1y0iA77eSff/69ICcDZ34uJj8Hc+rPglzIz/mzV9T681S4dfL6VMtx8rWbF5aHDw5PH9w8fXB4+oKHz8nJOxC8g8An6LQ/K59cplPrIlLOlPoe0tzcXGJjY3nssccKze/RowcrVqywI5KIVAQOB/iFnJxocM5mbn9OIiJSMmwpSJOSkigoKCA8PLzQ/PDwcBISEs5on5OTQ07O/66zSks7cxxDERERESmbbL0g6fShWIwxZx2e5YUXXiAwMNA1RUfr2ckiIiIi5YUtBWmVKlVwc3M7ozc0MTHxjF5TgMcff5zU1FTXdODAgZKKKiIiIiLFzJaC1NPTk1atWrFw4cJC8xcuXEjHjh3PaO/l5UVAQEChSURERETKB9uGfXrooYcYNmwYrVu3pkOHDrz//vvs37+fe+65x65IIiIiImID2wrSwYMHk5yczHPPPUd8fDyNGzdm7ty51KhRw65IIiIiImIDPTpURERERIpcqR+H9J86VUNr+CcRERGR0ulUnXYhfZ9lsiBNT08H0PBPIiIiIqVceno6gYGB521TJk/ZO51ODh8+jL+//1nHLS0OaWlpREdHc+DAAV0m8BfaL2en/XJu2jdnp/1ybto3Z6f9cm7aN2dX0vvFGEN6ejpRUVE4HOcf2KlM9pA6HA6qVatmy2dr2Kmz0345O+2Xc9O+OTvtl3PTvjk77Zdz0745u5LcL3/XM3qKrU9qEhERERFRQSoiIiIitlJBeoG8vLx45pln8PLysjtKqaL9cnbaL+emfXN22i/npn1zdtov56Z9c3aleb+UyZuaRERERKT8UA+piIiIiNhKBamIiIiI2EoFqYiIiIjYSgWpiIiIiNhKBemfnn/+eTp27Iivry9BQUFnbbN//3769euHn58fVapU4f777yc3N/e875uTk8OYMWOoUqUKfn5+9O/fn4MHDxbDFpSMJUuWYFnWWac1a9acc70RI0ac0b59+/YlmLz41axZ84xtfOyxx867jjGG8ePHExUVhY+PD126dGHz5s0llLhk7N27lzvuuIOYmBh8fHyoXbs2zzzzzN/+2ymPx8y7775LTEwM3t7etGrVil9++eW87ZcuXUqrVq3w9vamVq1aTJ48uYSSlpwXXniBNm3a4O/vT1hYGAMGDGD79u3nXedc/w9t27athFIXv/Hjx5+xfREREeddpyIcL3D2/2sty2LUqFFnbV9ej5dly5bRr18/oqKisCyL2bNnF1p+qd8vM2fOpGHDhnh5edGwYUNmzZpVTFtQmArSP+Xm5nLjjTdy7733nnV5QUEB11xzDZmZmSxfvpwZM2Ywc+ZMxo0bd973HTt2LLNmzWLGjBksX76cjIwM+vbtS0FBQXFsRrHr2LEj8fHxhaY777yTmjVr0rp16/Ou26tXr0LrzZ07t4RSl5znnnuu0Db+61//Om/7l19+mddff523336bNWvWEBERQffu3UlPTy+hxMVv27ZtOJ1O3nvvPTZv3szEiROZPHkyTzzxxN+uW56OmS+//JKxY8fy5JNPsm7dOjp16kTv3r3Zv3//WdvHxcXRp08fOnXqxLp163jiiSe4//77mTlzZgknL15Lly5l1KhRrFq1ioULF5Kfn0+PHj3IzMz823W3b99e6PioW7duCSQuOY0aNSq0fRs3bjxn24pyvACsWbOm0H5ZuHAhADfeeON51ytvx0tmZibNmjXj7bffPuvyS/l+WblyJYMHD2bYsGFs2LCBYcOGMWjQIFavXl1cm/E/RgqZOnWqCQwMPGP+3LlzjcPhMIcOHXLN++KLL4yXl5dJTU0963ulpKQYDw8PM2PGDNe8Q4cOGYfDYebNm1fk2e2Qm5trwsLCzHPPPXfedsOHDzfXXnttyYSySY0aNczEiRMvuL3T6TQRERHmxRdfdM3Lzs42gYGBZvLkycWQsPR4+eWXTUxMzHnblLdjpm3btuaee+4pNK9BgwbmscceO2v7Rx55xDRo0KDQvLvvvtu0b9++2DKWBomJiQYwS5cuPWebxYsXG8AcP3685IKVsGeeecY0a9bsgttX1OPFGGMeeOABU7t2beN0Os+6vCIcL4CZNWuW6/Wlfr8MGjTI9OrVq9C8nj17miFDhhR55tOph/QCrVy5ksaNGxMVFeWa17NnT3JycoiNjT3rOrGxseTl5dGjRw/XvKioKBo3bsyKFSuKPXNJmDNnDklJSYwYMeJv2y5ZsoSwsDDq1avHyJEjSUxMLP6AJeyll14iJCSE5s2b8/zzz5/3tHRcXBwJCQmFjg8vLy86d+5cbo6Pc0lNTSU4OPhv25WXYyY3N5fY2NhCP2uAHj16nPNnvXLlyjPa9+zZk7Vr15KXl1dsWe2WmpoKcEHHR4sWLYiMjKRbt24sXry4uKOVuJ07dxIVFUVMTAxDhgxhz54952xbUY+X3NxcPvvsM26//XYsyzpv2/J+vPzVpX6/nOs4KonvJBWkFyghIYHw8PBC8ypXroynpycJCQnnXMfT05PKlSsXmh8eHn7OdcqaKVOm0LNnT6Kjo8/brnfv3nz++ef8/PPPvPbaa6xZs4arrrqKnJycEkpa/B544AFmzJjB4sWLGT16NG+88Qb33XffOdufOgZOP67K0/FxNrt37+att97innvuOW+78nTMJCUlUVBQcFE/67P9nxMeHk5+fj5JSUnFltVOxhgeeughrrjiCho3bnzOdpGRkbz//vvMnDmTb7/9lvr169OtWzeWLVtWgmmLV7t27fjkk0+YP38+H3zwAQkJCXTs2JHk5OSztq+IxwvA7NmzSUlJOW+nSEU4Xk53qd8v5zqOSuI7yb3YP8FG48eP59lnnz1vmzVr1vzttY+nnO23L2PM3/5WVhTrFLdL2VcHDx5k/vz5fPXVV3/7/oMHD3b9vXHjxrRu3ZoaNWrwww8/MHDgwEsPXswuZr88+OCDrnlNmzalcuXK3HDDDa5e03M5/VgojcfH2VzKMXP48GF69erFjTfeyJ133nnedcvqMXM+F/uzPlv7s80vL0aPHs0ff/zB8uXLz9uufv361K9f3/W6Q4cOHDhwgFdffZUrr7yyuGOWiN69e7v+3qRJEzp06EDt2rX5+OOPeeihh866TkU7XuBkp0jv3r0Lnb08XUU4Xs7lUr5f7PpOKtcF6ejRoxkyZMh529SsWfOC3isiIuKMi3qPHz9OXl7eGb9N/HWd3Nxcjh8/XqiXNDExkY4dO17Q55aUS9lXU6dOJSQkhP79+1/050VGRlKjRg127tx50euWpH9yDJ26I3zXrl1nLUhP3TGbkJBAZGSka35iYuI5j6nS5GL3zeHDh+natSsdOnTg/fffv+jPKyvHzNlUqVIFNze3M3oZzvezjoiIOGt7d3f38/6CU1aNGTOGOXPmsGzZMqpVq3bR67dv357PPvusGJKVDn5+fjRp0uScx39FO14A9u3bx6JFi/j2228vet3yfrxc6vfLuY6jkvhOKtcFaZUqVahSpUqRvFeHDh14/vnniY+Pd/1wFyxYgJeXF61atTrrOq1atcLDw4OFCxcyaNAgAOLj49m0aRMvv/xykeQqKhe7r4wxTJ06lVtvvRUPD4+L/rzk5GQOHDhQ6B9KafRPjqF169YBnHMbY2JiiIiIYOHChbRo0QI4eT3U0qVLeemlly4tcAm6mH1z6NAhunbtSqtWrZg6dSoOx8VfLVRWjpmz8fT0pFWrVixcuJDrrrvONX/hwoVce+21Z12nQ4cOfPfdd4XmLViwgNatW1/Sv7nSyhjDmDFjmDVrFkuWLCEmJuaS3mfdunVl8ti4UDk5OWzdupVOnTqddXlFOV7+aurUqYSFhXHNNddc9Lrl/Xi51O+XDh06sHDhwkJn/BYsWFAynWjFfttUGbFv3z6zbt068+yzz5pKlSqZdevWmXXr1pn09HRjjDH5+fmmcePGplu3bub33383ixYtMtWqVTOjR492vcfBgwdN/fr1zerVq13z7rnnHlOtWjWzaNEi8/vvv5urrrrKNGvWzOTn55f4NhalRYsWGcBs2bLlrMvr169vvv32W2OMMenp6WbcuHFmxYoVJi4uzixevNh06NDBVK1a1aSlpZVk7GKzYsUK8/rrr5t169aZPXv2mC+//NJERUWZ/v37F2r31/1ijDEvvviiCQwMNN9++63ZuHGjuemmm0xkZGS52S/GnBxZok6dOuaqq64yBw8eNPHx8a7pr8r7MTNjxgzj4eFhpkyZYrZs2WLGjh1r/Pz8zN69e40xxjz22GNm2LBhrvZ79uwxvr6+5sEHHzRbtmwxU6ZMMR4eHuabb76xaxOKxb333msCAwPNkiVLCh0bJ06ccLU5fd9MnDjRzJo1y+zYscNs2rTJPPbYYwYwM2fOtGMTisW4cePMkiVLzJ49e8yqVatM3759jb+/f4U/Xk4pKCgw1atXN48++ugZyyrK8ZKenu6qVQDXd9C+ffuMMRf2/TJs2LBCI338+uuvxs3Nzbz44otm69at5sUXXzTu7u5m1apVxb49Kkj/NHz4cAOcMS1evNjVZt++feaaa64xPj4+Jjg42IwePdpkZ2e7lsfFxZ2xTlZWlhk9erQJDg42Pj4+pm/fvmb//v0luGXF46abbjIdO3Y853LATJ061RhjzIkTJ0yPHj1MaGio8fDwMNWrVzfDhw8vF/vhlNjYWNOuXTsTGBhovL29Tf369c0zzzxjMjMzC7X7634x5uTQHM8884yJiIgwXl5e5sorrzQbN24s4fTFa+rUqWf9t3X678MV4Zh55513TI0aNYynp6dp2bJloaGNhg8fbjp37lyo/ZIlS0yLFi2Mp6enqVmzppk0aVIJJy5+5zo2/vrv5PR989JLL5natWsbb29vU7lyZXPFFVeYH374oeTDF6PBgwebyMhI4+HhYaKioszAgQPN5s2bXcsr6vFyyvz58w1gtm/ffsayinK8nBrO6vRp+PDhxpgL+37p3Lmzq/0pX3/9talfv77x8PAwDRo0KLHC3TLmz6ueRURERERsoGGfRERERMRWKkhFRERExFYqSEVERETEVipIRURERMRWKkhFRERExFYqSEVERETEVipIRURERMRWKkhFRERExFYqSEVERETEVipIRURERMRWKkhFRERExFYqSEVERETEVv8f+GaoTHCARNIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train(learning_rate=0.0001,batch_size = 10,note=\"10-batch-GD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "70ba01cf-e65b-42bf-8dd9-40c8b4a1506c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "最终系数为： 2.015854531184876 2.9998966422578417 3.988713399434743\n",
      "最后迭代次数： 20036\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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g3rx5GDhwIEaPHg0A6NevH8aOHYvp06fjpZdeAuBf7is7OxtXXXUVACArKwv9+/dHTk4OnnrqKZw7dw7z5s3D9OnTuXQXERERdRhqqE1OTobdbu9Qm0oJIVBdXY2SkhIA0H3i3xZBBdtVq1YBAEaNGqW7//XXX8fUqVMBAPPnz0dNTQ1mzJiB0tJSDBkyBFu2bNGtPbZixQqYTCZMmjQJNTU1uOmmm7B69WpdN/TatWsxe/ZsbfWECRMmYOXKldpxo9GId999FzNmzMCIESNgs9kwefJkPP3000E1QDSVVnngkRWkxMdEuypERER0AZJlWQu1iYmJ0a5Ou7DZbAD8w1KTk5NDGpYgCSFEuCp2sSkvL4fD4YDL5YpKL+/Ipz7CuUoPdi8YDZslPGNLiIiIqOOora3F0aNHcemll2oBsCOqqanB999/j969eyMmRt/hF0xeC2kdW2o7IQSOna1GhduHc9WeaFeHiIiILmAdafhBU8J1fgy2USIr9R3lHp8SxZoQERERdQwMtlHiCwi2XpnBloiIiChUDLZR4mOPLREREVFYMdhGiS+gl9bDHlsiIiKikDHYRoluKAJ7bImIiKgDOX36NJxOJ5YuXardt2vXLlgsFmzZsqXdXrdNW+pS6HxywFAE9tgSERFRKwghUOOVo/LaNrOx1asXdO/eHa+99hpuu+02ZGVloW/fvrj77rsxY8YMbY+C9sBgGyWBE8Y4eYyIiIhao8Yro///fhCV1z70+BjYLa2PjrfccgumT5+Ou+66C9dddx1iYmLwxBNPtGMNORQharjcFxEREXV0Tz/9NHw+HzZs2IC1a9c22nwh3NhjGyU+JXDyWKfd/I2IiIiCYDMbcejxMVF77WB99913OHnyJBRFwbFjxzBo0KB2qFk9Btso4eQxIiIiCpYkSUENB4gmj8eDu+66C7fffjv69u2LadOmYf/+/UhJSWm31+RQhCjh5DEiIiLqyBYsWACXy4U//elPmD9/Pvr164dp06a162sy2EYJJ48RERFRR/Xxxx/jueeew5o1axAfHw+DwYA1a9Zg27ZtWLVqVbu97sXRl90BcfIYERERdVSjRo2C1+vV3Zeeno6ysrJ2fV322EaJl0MRiIiIiMKKwTZKZN3kMa6KQERERBQqBtso8eqW+4rODiJEREREHQmDbZQErorg5Tq2RERERCFjsI0SObDHlpPHiIiIiELGYBslnDxGREREraUoHTsrhOv8uNxXlMjceYyIiIhaYLFYYDAYcPLkSXTv3h0WiwWSJEW7WmEjhIDH48Hp06dhMBhgsVhCej4G2ygJ3JSBPbZERETUFIPBgN69e6OoqAgnT56MdnXajd1uR3p6OgyG0AYTMNhGiS+wx5bBloiIiJphsViQnp4On88HuQOupGQ0GmEymcLSE81gGyU+3c5jXBWBiIiImidJEsxmM8xmc7SrckHj5LEo8XEoAhEREVFYMdhGCSePEREREYUXg22UcLkvIiIiovBisI2SwKEInDxGREREFDoG2yjRTx5jsCUiIiIKFYNtlPgUTh4jIiIiCicG2yjxyVzHloiIiCicGGyjRLdBA9exJSIiIgoZg22UcB1bIiIiovBisI0SH9exJSIiIgorBtsoCRxj62aPLREREVHIGGyjxKvo17EVguNsiYiIiELBYBslgVvqCqH/mYiIiIiCx2AbJYFDEQBOICMiIiIKFYNtlARu0ABwyS8iIiKiUDHYRknDHlu3LEepJkREREQdA4NtlHgbjKn1yuyxJSIiIgoFg22UyI2GInCMLREREVEoGGyjpGEPLSePEREREYUm6GD7ySefYPz48UhLS4MkSdi8ebPu+NSpUyFJku42dOhQXRm3241Zs2YhKSkJsbGxmDBhAk6cOKErU1paipycHDgcDjgcDuTk5KCsrExX5vjx4xg/fjxiY2ORlJSE2bNnw+PxBHtKUdFweS8Pe2yJiIiIQhJ0sK2qqsLVV1+NlStXNltm7NixKCoq0m7vvfee7nhubi42bdqE9evXY9u2baisrER2djbkgAlUkydPxr59+5CXl4e8vDzs27cPOTk52nFZlnHrrbeiqqoK27Ztw/r16/H3v/8dc+fODfaUosLXoIfWyx5bIiIiopCYgn3AuHHjMG7cuPOWsVqtcDqdTR5zuVx49dVXsWbNGowePRoA8Oabb6Jnz5748MMPMWbMGBw+fBh5eXnYuXMnhgwZAgB45ZVXMGzYMBw5cgRXXXUVtmzZgkOHDqGwsBBpaWkAgGeeeQZTp07FkiVLEB8fH+ypRVSjoQjssSUiIiIKSbuMsf3444+RnJyMK6+8EtOnT0dJSYl2rKCgAF6vF1lZWdp9aWlpyMjIwPbt2wEAO3bsgMPh0EItAAwdOhQOh0NXJiMjQwu1ADBmzBi43W4UFBQ0WS+3243y8nLdLVoaDkXgqghEREREoQl7sB03bhzWrl2Lf//733jmmWewZ88e/PSnP4Xb7QYAFBcXw2KxoFu3brrHpaSkoLi4WCuTnJzc6LmTk5N1ZVJSUnTHu3XrBovFopVpaNmyZdqYXYfDgZ49e4Z8vm3lbbAqgofr2BIRERGFJOihCC25/fbbte8zMjIwePBg9OrVC++++y4mTpzY7OOEEJAkSfs58PtQygR6+OGHMWfOHO3n8vLyqIVbdYMGSQKEADzceYyIiIgoJO2+3Fdqaip69eqFb775BgDgdDrh8XhQWlqqK1dSUqL1wDqdTpw6darRc50+fVpXpmHPbGlpKbxeb6OeXJXVakV8fLzuFi3qUAS72QiAk8eIiIiIQtXuwfbs2bMoLCxEamoqACAzMxNmsxn5+flamaKiIhw4cADDhw8HAAwbNgwulwu7d+/WyuzatQsul0tX5sCBAygqKtLKbNmyBVarFZmZme19WiFTg6zN4u805+QxIiIiotAEPRShsrIS3377rfbz0aNHsW/fPiQkJCAhIQGLFi3Cz3/+c6SmpuL777/HH/7wByQlJeFnP/sZAMDhcGDatGmYO3cuEhMTkZCQgHnz5mHgwIHaKgn9+vXD2LFjMX36dLz00ksAgHvvvRfZ2dm46qqrAABZWVno378/cnJy8NRTT+HcuXOYN28epk+ffsGviAAE9Nha2GNLREREFA5BB9vPPvsMN954o/azOmZ1ypQpWLVqFfbv34+//OUvKCsrQ2pqKm688Ua89dZbiIuL0x6zYsUKmEwmTJo0CTU1NbjpppuwevVqGI1GrczatWsxe/ZsbfWECRMm6NbONRqNePfddzFjxgyMGDECNpsNkydPxtNPPx18K0SBGmTVYMudx4iIiIhCIwkhOu2spfLycjgcDrhcroj38vb/3zxUe2Rcm94Vnx8vwyO39sM9N1wW0ToQERERXeiCyWvtPsaWmuZrNBSh015fEBEREYUFg22UqFvq2sycPEZEREQUDgy2UaAoAurGY5w8RkRERBQeDLZR4AvYTpfBloiIiCg8GGyjwBewna6tLti6ORSBiIiIKCQMtlHAHlsiIiKi8GOwjQKfHBhsOXmMiIiIKBwYbKNAHYogSYDV5P8VsMeWiIiIKDQMtlGg9tiaDQZYtGDLdWyJiIiIQsFgGwVqsDUaJJiN/l8BJ48RERERhYbBNgrUoQgmowSLkUMRiIiIiMKBwTYK1FURzEYDzHVDETh5jIiIiCg0DLZRoPbOGg3ssSUiIiIKFwbbKJDVHluDBItJAsBgS0RERBQqBtsoUFdAMBo5eYyIiIgoXBhso6C+x9bAoQhEREREYcJgGwU+uX5VBG3yGIMtERERUUgYbKPAq6jr2Ab02Pq4QQMRERFRKBhso0CuW8fWbJQCdh5jjy0RERFRKBhso8DbxM5jXMeWiIiIKDQMtlGgmzzGMbZEREREYcFgGwXewMljRq5jS0RERBQODLZR4AsYiqBOHlNE/WoJRERERBQ8Btso0IYiGOuHIgD1Y2+JiIiIKHgMtlHgrVsVwRQweQzgBDIiIiKiUDDYRoHaY2sySjAZJEj+YbacQEZEREQUAgbbKFCHHJgMBkhSfa8tJ5ARERERtR2DbRRoW+oa/F21Fq5lS0RERBQyBtso8AUMRQDA3ceIiIiIwoDBNgrU5b5MdT216lq2bvbYEhEREbUZg20U+BT9UASOsSUiIiIKHYNtFGhDEQz+5q8fisB1bImIiIjaisE2CnwBW+oCnDxGREREFA4MtlFQ32PLyWNERERE4cJgGwWNJ4/V9dgy2BIRERG1GYNtFDSePOb/yqEIRERERG3HYBsF9T226lAEIwAORSAiIiIKBYNtFKhjbM3qqgjssSUiIiIKGYNtFKjB1sjJY0RERERhw2AbBepyX+rY2vrJY1zHloiIiKitGGyjQN2IwWhosCoChyIQERERtRmDbRTISoMNGjgUgYiIiChkDLZRoE0e485jRERERGETdLD95JNPMH78eKSlpUGSJGzevFl3XAiBRYsWIS0tDTabDaNGjcLBgwd1ZdxuN2bNmoWkpCTExsZiwoQJOHHihK5MaWkpcnJy4HA44HA4kJOTg7KyMl2Z48ePY/z48YiNjUVSUhJmz54Nj8cT7ClFnK/RUAR/wGWPLREREVHbBR1sq6qqcPXVV2PlypVNHl++fDmeffZZrFy5Env27IHT6cTNN9+MiooKrUxubi42bdqE9evXY9u2baisrER2djZkWdbKTJ48Gfv27UNeXh7y8vKwb98+5OTkaMdlWcatt96KqqoqbNu2DevXr8ff//53zJ07N9hTijh1gwZzg1URuPMYERERUduZgn3AuHHjMG7cuCaPCSHw3HPPYcGCBZg4cSIA4I033kBKSgrWrVuH3/zmN3C5XHj11VexZs0ajB49GgDw5ptvomfPnvjwww8xZswYHD58GHl5edi5cyeGDBkCAHjllVcwbNgwHDlyBFdddRW2bNmCQ4cOobCwEGlpaQCAZ555BlOnTsWSJUsQHx/fpgaJhPrJYw1WReBQBCIiIqI2C+sY26NHj6K4uBhZWVnafVarFSNHjsT27dsBAAUFBfB6vboyaWlpyMjI0Mrs2LEDDodDC7UAMHToUDgcDl2ZjIwMLdQCwJgxY+B2u1FQUNBk/dxuN8rLy3W3aJC1MbZ1GzRw8hgRERFRyMIabIuLiwEAKSkpuvtTUlK0Y8XFxbBYLOjWrdt5yyQnJzd6/uTkZF2Zhq/TrVs3WCwWrUxDy5Yt08bsOhwO9OzZsw1nGTo1wJoaTB7zch1bIiIiojZrl1URJEnS/SyEaHRfQw3LNFW+LWUCPfzww3C5XNqtsLDwvHVqL7LCoQhERERE4RbWYOt0OgGgUY9pSUmJ1rvqdDrh8XhQWlp63jKnTp1q9PynT5/WlWn4OqWlpfB6vY16clVWqxXx8fG6WzT4mhmKwMljRERERG0X1mDbu3dvOJ1O5Ofna/d5PB5s3boVw4cPBwBkZmbCbDbryhQVFeHAgQNamWHDhsHlcmH37t1amV27dsHlcunKHDhwAEVFRVqZLVu2wGq1IjMzM5ynFXbaUAT22BIRERGFTdCrIlRWVuLbb7/Vfj569Cj27duHhIQEpKenIzc3F0uXLkWfPn3Qp08fLF26FHa7HZMnTwYAOBwOTJs2DXPnzkViYiISEhIwb948DBw4UFsloV+/fhg7diymT5+Ol156CQBw7733Ijs7G1dddRUAICsrC/3790dOTg6eeuopnDt3DvPmzcP06dMv6BURgPqhCCYDJ48RERERhUvQwfazzz7DjTfeqP08Z84cAMCUKVOwevVqzJ8/HzU1NZgxYwZKS0sxZMgQbNmyBXFxcdpjVqxYAZPJhEmTJqGmpgY33XQTVq9eDaPRqJVZu3YtZs+era2eMGHCBN3auUajEe+++y5mzJiBESNGwGazYfLkyXj66aeDb4UIUyeJ1U8e4wYNRERERKGShBCddip+eXk5HA4HXC5XRHt5r3l8C8qqvcj/3U/QJyUO/zp8CtPe+AxX93DgH/dfH7F6EBEREV3ogslr7bIqAp2frPXYNpw81mmvMYiIiIhCxmAbBV6lucljcrOPISIiIqLzY7CNAm3ymFEfbLlBAxEREVHbMdhGmBCifvJY3aoIVq6KQERERBQyBtsIU3trAa5jS0RERBRODLYR5gsMtupyX9x5jIiIiChkDLYRFhhs1Z5aM9exJSIiIgoZg22EyQETxIwGdYMGDkUgIiIiChWDbYSpS30B9WNs1aEIitCPwSUiIiKi1mOwjTCftiKCBEnSTx4D2GtLRERE1FYMthHmq+uxVYchAPU9tgAnkBERERG1FYNthKk9toG9tKaAkMsJZERERERtw2AbYeqqCIE9tpIkcQIZERERUYgYbCNMHYqgLvGlsnD3MSIiIqKQMNhGmK/BdroqNeiyx5aIiIiobRhsI6ypoQhAwLa67LElIiIiahMG2wjzyS0NReA6tkRERERtwWAbYWpwbdhjy8ljRERERKFhsI0wdWexwOW+AE4eIyIiIgoVg22EqVvqmozNjLFljy0RERFRmzDYRpisDUVoZlUE9tgSERERtQmDbYRp69g2HGPLoQhEREREIWGwjbDmJo9xKAIRERFRaBhsI6y5yWNW9tgSERERhYTBNsLU4Nrs5DGuY0tERETUJgy2Eab22Jo4FIGIiIgorBhsI8yrBVuuY0tEREQUTgy2EeZraSgCe2yJiIiI2oTBNsKaG4pgqQu67LElIiIiahsG2whTl/syNbOlLjdoICIiImobBtsIk9UtdTl5jIiIiCisGGwjrL7HljuPEREREYUTg22E+bQeW33Ts8eWiIiIKDQMthHma3bymNpjyw0aiIiIiNqCwTbCfJw8RkRERNQuGGwjTFvHlpPHiIiIiMKKwTbCtKEInDxGREREFFYMthGmDkUwGxtOHuMGDUREREShYLCNMLXH1tjM5DEORSAiIiJqGwbbCPM1s0FD/eQxropARERE1BYMthHW/FAE9tgSERERhYLBNsLUHtuGQxHMRk4eIyIiIgoFg22E1ffYclUEIiIionAKe7BdtGgRJEnS3ZxOp3ZcCIFFixYhLS0NNpsNo0aNwsGDB3XP4Xa7MWvWLCQlJSE2NhYTJkzAiRMndGVKS0uRk5MDh8MBh8OBnJwclJWVhft0wq5+8pi+6e0WIwCgtMoDReE4WyIiIqJgtUuP7YABA1BUVKTd9u/frx1bvnw5nn32WaxcuRJ79uyB0+nEzTffjIqKCq1Mbm4uNm3ahPXr12Pbtm2orKxEdnY2ZFnWykyePBn79u1DXl4e8vLysG/fPuTk5LTH6YSVOhShYY/tFcld0MVqQnmtD4eKyqNRNSIiIqKLmqldntRk0vXSqoQQeO6557BgwQJMnDgRAPDGG28gJSUF69atw29+8xu4XC68+uqrWLNmDUaPHg0AePPNN9GzZ098+OGHGDNmDA4fPoy8vDzs3LkTQ4YMAQC88sorGDZsGI4cOYKrrrqqPU4rLLzqlrqGxpPHhl6WgA8Pl2Dbt2eQcYkjGtUjIiIiumi1S4/tN998g7S0NPTu3Rt33HEHvvvuOwDA0aNHUVxcjKysLK2s1WrFyJEjsX37dgBAQUEBvF6vrkxaWhoyMjK0Mjt27IDD4dBCLQAMHToUDodDK3OhkptZxxYARlyRBAD4z7dnIlonIiIioo4g7D22Q4YMwV/+8hdceeWVOHXqFBYvXozhw4fj4MGDKC4uBgCkpKToHpOSkoJjx44BAIqLi2GxWNCtW7dGZdTHFxcXIzk5udFrJycna2Wa4na74Xa7tZ/LyyP/kb9PbnooAgDc0McfbHcfPYdar4wYszGidSMiIiK6mIW9x3bcuHH4+c9/joEDB2L06NF49913AfiHHKgkSR/qhBCN7muoYZmmyrf0PMuWLdMmmzkcDvTs2bNV5xROze08BgCXd++ClHgr3D4FBcdKI101IiIiootauy/3FRsbi4EDB+Kbb77Rxt027FUtKSnRenGdTic8Hg9KS0vPW+bUqVONXuv06dONeoMDPfzww3C5XNqtsLAwpHNri+Y2aAD8YV0djrCNwxGIiIiIgtLuwdbtduPw4cNITU1F79694XQ6kZ+frx33eDzYunUrhg8fDgDIzMyE2WzWlSkqKsKBAwe0MsOGDYPL5cLu3bu1Mrt27YLL5dLKNMVqtSI+Pl53izRvM1vqqq7nOFsiIiKiNgn7GNt58+Zh/PjxSE9PR0lJCRYvXozy8nJMmTIFkiQhNzcXS5cuRZ8+fdCnTx8sXboUdrsdkydPBgA4HA5MmzYNc+fORWJiIhISEjBv3jxtaAMA9OvXD2PHjsX06dPx0ksvAQDuvfdeZGdnX9ArIgD1k8dMTYyxBeqD7f4fXCir9qCr3RKxuhERERFdzMIebE+cOIE777wTZ86cQffu3TF06FDs3LkTvXr1AgDMnz8fNTU1mDFjBkpLSzFkyBBs2bIFcXFx2nOsWLECJpMJkyZNQk1NDW666SasXr0aRmP9ZKq1a9di9uzZ2uoJEyZMwMqVK8N9OmHna2a5L1VyfAyuTOmCr09VYvt/z+KWgamRrB4RERHRRUsSQnTaba7Ky8vhcDjgcrkiNizhx0s+REmFG+/Ovh4D0ppeq/axdw7i9f98j8lD0rH0ZwMjUi8iIiKiC1Ewea3dx9iSnjYUoZkeW6B+2S+OsyUiIiJqPQbbCPPWrWPb3BhbAPhx70SYDBKOna1G4bnqSFWNiIiI6KLGYBth9T22zQfbLlYTrk3vCoDLfhERERG1FoNthHm1VRHO3/Tqera7vjvb7nUiIiIi6ggYbCNM21L3PD22ANAn2b9KxInSmnavExEREVFHwGAbQYoiUNdh2+SWuoGcjhgAQJGrtr2rRURERNQhMNhGkE+pX1mtpaEIqXXBtqSiForSaVdkIyIiImo1BtsIkgODbQs9tt3jrJAkwCsLnK3ytHfViIiIiC56DLYR5FUU7fvzLfcFAGajAd27WAEAp8o5HIGIiIioJQy2EaRupwsA5vNs0KDiOFsiIiKi1mOwjSBfXY+tJAGGFoYiAIAz3h9si11cGYGIiIioJQy2EaT22Lamtxaon0BWzKEIRERERC1isI0gbdexFsbXqlI4FIGIiIio1RhsI8hbtzlDS2vYqrQeWwZbIiIiohYx2EaQuo6tuYU1bFXOeBsADkUgIiIiag0G2whSx9i2tsfWGdBjKwQ3aSAiIiI6HwbbCFJXRTC3NtjWrYpQ7ZFR4fa1W72IiIiIOgIG2wjyaZPHWtfsNosRDpsZAMfZEhEREbWEwTaC1KEILW2nGyiVKyMQERERtQqDbQT56lZFaO1yX0D9ONtTDLZERERE58VgG0HqUARjKzdoAOrH2bLHloiIiOj8GGwjSJs81oYe2+JybqtLREREdD4MthHkbcMYW7XHlpPHiIiIiM6PwTaCtC11gxmKwMljRERERK3CYBtB3jZMHkt1+HcfO8Xdx4iIiIjOi8E2gmQluJ3HgPqhCKXVXtR65XapFxEREVFHwGAbQeo6tuZWbtAAAPE2E2xmIwCOsyUiIiI6HwbbCPLWrYoQzOQxSZK0TRqKORyBiIiIqFkMthGkTR4LYowtAKRwZQQiIiKiFjHYRlD9cl/BNTu31SUiIiJqGYNtBMlK8KsiAECKuq0uhyIQERERNYvBNoLaskEDENhjy93HiIiIiJrDYBtB6qoIpiBWRQACdh8rd4e9TkREREQdBYNtBMltWBUBqN99rJg9tkRERETNYrCNIG8bttQF6oPt6Qo3fHW7lxERERGRHoNtBKnLfZmDnDyWFGuFySBBEcDpSg5HICIiImoKg20Eeet6W4PZUhcADAZJW8uWS34RERERNY3BNoLaOnkMqB+OcIrBloiIiKhJDLYR5FPattwXUL/k16vbjqKkguGWiIiIqCEG2whSJ34Fu0EDAPxqxKWItRjx2bFSZP9pG/Z8fy7c1SMiIiK6qDHYRpDaY2sOclUEAMjslYB/3H89+iR3QUmFG3e8vBMvbv0vajxyuKtJREREdFFisI0gNdgGO3lMdUVyF2yeOQITrk6DrAg88f5X+PGSD/GHTfuxr7AMQohwVpeIiIjoomKKdgU6E3UoQrDLfQWKtZrwxzuuwdDLEvHCx9/iRGkN1u06jnW7jiPNEYN+qfHomxqHq5zxuKSrDQmxFiTEWhAf4/9Vy4qATxGodPtQeK4ax89Vo/BcNTw+BWldbbikmw2XdLXB6YiB3RLePw8hBIrLa+GTBSTJH/CtJiO62c2QpPO3iVdWUFbtRVe7GeY2TL4jIiKiju+iD7YvvPACnnrqKRQVFWHAgAF47rnncMMNN0S7Wk3SJo+FGMwkScLkIem447qe2Hn0LDbsKcT7B4px0lWLk65a/OurkkaPMUiAEmSHrs1sRGIXCxJjLYAkQVYU+GQBr6xAVgS8soBPCfheVuBTBOJizLi8eyyuSO6Cy7p3wZlKN/afcGH/Dy64aryNXqeb3YwrU+LQ1xmHpC5WnK3y4Eylu+7m/76s2v84s1HC5d27oK8zDpd37wIBoNYro8Yrw+1TIMv+4C4rSt1XoX2NizHhkq42pHW1wRkfgwq3F8UuN06V16Ki1ofLk2ORkebAgLR4JHaxNqqnEPXPFfi89T8rUBRAQMBuMaGL1YQYs/93XeH2oazKi7IaD4wGCQmxFnSzWxBjNjbZ9rIiUFHrRa1Xgd1qRKzFdN6efo9PQWm1B7FWE2ItxhYvFIiIiDqiizrYvvXWW8jNzcULL7yAESNG4KWXXsK4ceNw6NAhpKenR7t6jfjauI5tcwwGCcMvT8Lwy5Ow2O3DwR9c+Kq4Al8VV+BIcTlOV7pxrtKDKo/cKNRKEuCMj0HPBDvSE+ywmAw4WVaDk2U1+KG0BlUef1g8UVqDE6XBbeXrrgulu442nuBmMkgwGw1QhIAQgEdWUFrtxa6j55os35BXFto5tqc4qwkC0IK7rIigLwyA+t+13MyDbWYjbBaj1i4GA1Be40N5rRcNR5bYLUZ0sfoDc5cYE2ItprpwXoszlR6tnNVkQGKsBYldrEiItWgXJ2ajAeeqPDhT6cHZKjfcXv/foyT5bzEmI+xWE7pYjbCZTQj8M5UVgRqvjGqPjBqPDKNBQkq8FSmOGKTExaC02oNvTlXi65IKHD9bje5xVvRJicOVyV3QM8GOs1UenHLVoqi8FrVeGamOGKTVXWRYTQaU13hRUes/74pan/ZztceHeJsZibEWJHWxIinO6v/axf9zF6sJvrqLCp9cf8HhUy++lPoLLl/dhZhX9l/4BF6MBV6kKEJAUQTibWbtQkhdlcTtU+D2yaj1Ktr3bp+/HR02M7razHDYzACA8rrzqHT7YLcY6+pthc1ihBACtV4FVR4far36cfLqpxitvQCWFYHKurZThEBKfEyzF0ytoSgC5bVeeHwKusSYYDPzQomILh6SuIgHZg4ZMgQ/+tGPsGrVKu2+fv364bbbbsOyZctafHx5eTkcDgdcLhfi4+Pbs6oAgJxXd+HTb85gxe1X42fX9mj311PVemWU13ghSRLMRgkmowFWk+G8H+lXuX04W+nBmSp/OBbwr+ZgMkgwGQwwGyUY68KY/36D/5hRwrkqD74tqcS3JZU4eqYKXe1mDOrRFQMvceDKlDhYTAZd3b4tqdTCuKvGi8Qu+vCift/VbsHJshocKa7AkVMVOHqmCmajATazETFmA6wmo1ZHo6Huq9FfL6MkobTagx/qwntxeS3iY8xwxscgxREDu9mII6cqcOhkOb47UxV0G6uvaTRIEAKo8Tae1GczG9HVboZPESir9sArt/xPz2iQmg3FDbWlV54iz2oywCMrjS5cGnLYzEiItSDWaoTF6P/7NpsMqPH4UF7jQ0WtF+W1PlS6fY0e281uhtNhQ6zF2CiAGyQJBsn/1WiQINX9LCsC56o8OFfl0T5dAvx/g12sJpgMUsCnIAqMdY83GQ31/97qvkqSpPskwyhJiLEY/RdydRdzMXXfW00GeGUFtV4FNV4ZXlnx17HuucxGCXaLCTaLEXazEQaDBI9PgVdWbwIeWYHX579IMRslxNQ9r9VU97Xu/cGnCJTXeOGquwkhEGM2auW9skCtT4bbK8OnCHSzW7T3oViryf/pkEdGdd3XmroOgBqvDCGge18MvBCNMRu1Cy51a3WryVD32oZWLQHZmv+pBfwdKP7fuf9mkOD/XWnvjQYYJejeG411790GKeD3qP3s//0aJP+FXY1XRq1Xhsen/p6glbNb/L9bu8UIgyRpn57JSn0ngU8RgADibSY4bGY4bBZYTAZUBFzUynW/F//v0ACfIrT2rvXJkFD/fqu7Sf56q4+NMfvroQj1ghXahWmN1/97liT94w0G1J1z/b8R/XF/Gxnq3ush/J/SCf9pQQhR99V/P7T7myjXRIeTJEmQ6r431H0PCZDg/x0EHpckyf8V0P4dS/Dfp/5bb3T8Ir1IDSavXbQ9th6PBwUFBXjooYd092dlZWH79u1RqtX5qRs0GNuwKkIo1DfuYMRaTYi1mpCeaA/69Xp0s2NQj66trlvGJQ5kXOJoVfmeCXb0TLBjdP+UoOvVWhW1Xpwqd+ve4LU3f4Mh4I2v/g2uIUURqPL4UOX2B9yudrPudyCEf5xzaZUXbp/s/4+5rsfRYTPBYbOgq90Mk0GC26egyu0PMJVuHypr67+PizEhJT4GzvgYJMRaUOOVcbbSH07OVrlxttKDs3VhxeNTdD25dosR6vuqIgTcXhmVbhnVAfVWGSTU/adlgt1ihMen4FR5LYrLa1FS7kZcjMnfQ5vSBZcmxqKkohZfn6rEkeIKFLlqkNjFitS6iwiryYBiV63/04GyWvgUBfExZsTbTIiLMeu+t5uNcNV4cbaqblhKhRunK/3ndabSjWqP3OBixqD7nZmM/oswU10AU7+a68qo3xvrLswMBglGg/8/h3PVHu1TjJIKNyT4e1P9IUkfmhQFcNV4/T3NdUGzi9WE+Bh/73qVW8bpSjc8dWEjkMVkQOBfkBp61fDVWuqwl1qv/1OQ0urWP7Yp6oWSrIig6kFEF77A4CwFBOLA7/XB2v8psRqSJQA2ixHbHvxpNE+jSRdtsD1z5gxkWUZKij7gpKSkoLi4uMnHuN1uuN1u7efy8vJ2rWNDPqVu8liYhiJQ+4iLMSMuxhzScxgM0nmfR5LOfzyQemHS1LjfhuwWE+wJJvRMCP6CJJx6JtiR2SshqnUIJ0URWg9JS7yyAgmNx9KrFzNl1V5YzQbEWvwf8ze8MFKDpNp7Wu3xwe1T4Km72S1G/wWAdiHg/2oxGSCEQHmND0XlNSgqq4XbJ8NqNsJqNPgDdEBYVXuwFCEgCwGDJNVd+PgnnFqMBlR7ZFTU+nuHFQFdz6wQ+l64+q+KrqzaY6b2ktV4ZG1cfHXd9xajATEWI2JMhrrz8M9JUBR/b2yNR0aVx4cajwwBf8+o2ej/1MlSd/FiNvkvTryyqO+lbjBkRIL/ItNRN2REgoRan78Obq8Cs8mAGLWnzyChtMqD0xX+oVVVHtl/cWeu75W0W0xaz7MkQRva4pUVVLll7YK01ivDaDDAYvJffAkIuL0Kan0Kar1yWFe0MRvrL7wsJv9rNT8voOl5AtoQLCG0IT6yELCa/D3MNrMRZqNB63lUhIDXJ1Dt9WnDlYT6N2AM+ASt7gJSQKCi1v9vQR12ZTEaEG/z/z0b6y7oa+vmTqi98La690L/OaGuN9g/TEytu0dW4PbKqK3796JSg5rVZNCex2ryn0NgG8h1Q5FkoW8bRQQ/JC2wtzQwQEK7vz5Eqj26SoNeYCWgBzichABk3ZMG/wI2T9uHPLWnizbYqhr+RyOEaPY/n2XLluGxxx6LRLWa1DPBjvIanzYGj4guDk31yjenuSE+rb2YUScXJsRagqqj+hoOuxkOuxl9naEPr1I/uVG39CYKN/XiJZRx4ed7bgCtvihtDX+Q9wdprZcTjYcItAd1+EL9BUV9AAagzV0RAd8jIDDrhkkEfF8fnuse32DYhPZcWtj2H5dwYXbSXbTBNikpCUajsVHvbElJSaNeXNXDDz+MOXPmaD+Xl5ejZ8+e7VrPQM9OuiZir0VERHShMxgkxBjap+cvmAvS1pIkyT9GuZ3q3NJr12fmCzNUXggu2gVBLRYLMjMzkZ+fr7s/Pz8fw4cPb/IxVqsV8fHxuhsRERERdQwXbY8tAMyZMwc5OTkYPHgwhg0bhpdffhnHjx/HfffdF+2qEREREVGEXdTB9vbbb8fZs2fx+OOPo6ioCBkZGXjvvffQq1evaFeNiIiIiCLsol7HNlSRXseWiIiIiIITTF67aMfYEhEREREFYrAlIiIiog6BwZaIiIiIOoSLevJYqNThxZHegYyIiIiIWkfNaa2ZFtapg21FRQUARHSTBiIiIiIKXkVFBRwOx3nLdOpVERRFwcmTJxEXF9duW+AFUnc6Kyws5CoMrcD2Cg7bq/XYVsFhewWH7dV6bKvgdNb2EkKgoqICaWlpMBjOP4q2U/fYGgwG9OjRI+Kvy13PgsP2Cg7bq/XYVsFhewWH7dV6bKvgdMb2aqmnVsXJY0RERETUITDYEhEREVGHwGAbQVarFQsXLoTVao12VS4KbK/gsL1aj20VHLZXcNherce2Cg7bq2WdevIYEREREXUc7LElIiIiog6BwZaIiIiIOgQGWyIiIiLqEBhsiYiIiKhDYLCNoBdeeAG9e/dGTEwMMjMz8emnn0a7SlG3bNkyXHfddYiLi0NycjJuu+02HDlyRFdGCIFFixYhLS0NNpsNo0aNwsGDB6NU4wvHsmXLIEkScnNztfvYVno//PAD7r77biQmJsJut+Oaa65BQUGBdpztVc/n8+GRRx5B7969YbPZcNlll+Hxxx+Hoihamc7cXp988gnGjx+PtLQ0SJKEzZs36463pm3cbjdmzZqFpKQkxMbGYsKECThx4kQEzyIyztdWXq8XDz74IAYOHIjY2FikpaXhl7/8JU6ePKl7js7SVkDLf1uBfvOb30CSJDz33HO6+ztTe7WEwTZC3nrrLeTm5mLBggX4/PPPccMNN2DcuHE4fvx4tKsWVVu3bsXMmTOxc+dO5Ofnw+fzISsrC1VVVVqZ5cuX49lnn8XKlSuxZ88eOJ1O3HzzzaioqIhizaNrz549ePnllzFo0CDd/WyreqWlpRgxYgTMZjPef/99HDp0CM888wy6du2qlWF71XvyySfx4osvYuXKlTh8+DCWL1+Op556Cs8//7xWpjO3V1VVFa6++mqsXLmyyeOtaZvc3Fxs2rQJ69evx7Zt21BZWYns7GzIshyp04iI87VVdXU19u7di0cffRR79+7Fxo0b8fXXX2PChAm6cp2lrYCW/7ZUmzdvxq5du5CWltboWGdqrxYJiogf//jH4r777tPd17dvX/HQQw9FqUYXppKSEgFAbN26VQghhKIowul0iieeeEIrU1tbKxwOh3jxxRejVc2oqqioEH369BH5+fli5MiR4oEHHhBCsK0aevDBB8X111/f7HG2l96tt94qfv3rX+vumzhxorj77ruFEGyvQADEpk2btJ9b0zZlZWXCbDaL9evXa2V++OEHYTAYRF5eXsTqHmkN26opu3fvFgDEsWPHhBCdt62EaL69Tpw4IS655BJx4MAB0atXL7FixQrtWGdur6awxzYCPB4PCgoKkJWVpbs/KysL27dvj1KtLkwulwsAkJCQAAA4evQoiouLdW1ntVoxcuTITtt2M2fOxK233orRo0fr7mdb6b399tsYPHgwfvGLXyA5ORnXXnstXnnlFe0420vv+uuvx7/+9S98/fXXAIAvvvgC27Ztwy233AKA7XU+rWmbgoICeL1eXZm0tDRkZGR0+vZzuVyQJEn7NIVtpacoCnJycvD73/8eAwYMaHSc7aVninYFOoMzZ85AlmWkpKTo7k9JSUFxcXGUanXhEUJgzpw5uP7665GRkQEAWvs01XbHjh2LeB2jbf369di7dy/27NnT6BjbSu+7777DqlWrMGfOHPzhD3/A7t27MXv2bFitVvzyl79kezXw4IMPwuVyoW/fvjAajZBlGUuWLMGdd94JgH9f59OatikuLobFYkG3bt0alenM/w/U1tbioYcewuTJkxEfHw+AbdXQk08+CZPJhNmzZzd5nO2lx2AbQZIk6X4WQjS6rzO7//778eWXX2Lbtm2NjrHtgMLCQjzwwAPYsmULYmJimi3HtvJTFAWDBw/G0qVLAQDXXnstDh48iFWrVuGXv/ylVo7t5ffWW2/hzTffxLp16zBgwADs27cPubm5SEtLw5QpU7RybK/mtaVtOnP7eb1e3HHHHVAUBS+88EKL5TtjWxUUFOCPf/wj9u7dG/S5d8b2Ajh5LCKSkpJgNBobXTmVlJQ0usLvrGbNmoW3334bH330EXr06KHd73Q6AYBtB/8bXElJCTIzM2EymWAymbB161b86U9/gslk0tqDbeWXmpqK/v376+7r16+fNmGTf1t6v//97/HQQw/hjjvuwMCBA5GTk4Pf/e53WLZsGQC21/m0pm2cTic8Hg9KS0ubLdOZeL1eTJo0CUePHkV+fr7WWwuwrQJ9+umnKCkpQXp6uva+f+zYMcydOxeXXnopALZXQwy2EWCxWJCZmYn8/Hzd/fn5+Rg+fHiUanVhEELg/vvvx8aNG/Hvf/8bvXv31h3v3bs3nE6nru08Hg+2bt3a6drupptuwv79+7Fv3z7tNnjwYNx1113Yt28fLrvsMrZVgBEjRjRaOu7rr79Gr169APBvq6Hq6moYDPr/EoxGo7bcF9urea1pm8zMTJjNZl2ZoqIiHDhwoNO1nxpqv/nmG3z44YdITEzUHWdb1cvJycGXX36pe99PS0vD73//e3zwwQcA2F6NRGnSWqezfv16YTabxauvvioOHTokcnNzRWxsrPj++++jXbWo+u1vfyscDof4+OOPRVFRkXarrq7WyjzxxBPC4XCIjRs3iv3794s777xTpKamivLy8ijW/MIQuCqCEGyrQLt37xYmk0ksWbJEfPPNN2Lt2rXCbreLN998UyvD9qo3ZcoUcckll4h//vOf4ujRo2Ljxo0iKSlJzJ8/XyvTmduroqJCfP755+Lzzz8XAMSzzz4rPv/8c20mf2va5r777hM9evQQH374odi7d6/46U9/Kq6++mrh8/midVrt4nxt5fV6xYQJE0SPHj3Evn37dO/7brdbe47O0lZCtPy31VDDVRGE6Fzt1RIG2wj685//LHr16iUsFov40Y9+pC1p1ZkBaPL2+uuva2UURRELFy4UTqdTWK1W8ZOf/ETs378/epW+gDQMtmwrvXfeeUdkZGQIq9Uq+vbtK15++WXdcbZXvfLycvHAAw+I9PR0ERMTIy677DKxYMECXdjozO310UcfNfleNWXKFCFE69qmpqZG3H///SIhIUHYbDaRnZ0tjh8/HoWzaV/na6ujR482+77/0Ucfac/RWdpKiJb/thpqKth2pvZqiSSEEJHoGSYiIiIiak8cY0tEREREHQKDLRERERF1CAy2RERERNQhMNgSERERUYfAYEtEREREHQKDLRERERF1CAy2RERERNQhMNgSERERUYfAYEtEREREHQKDLRERERF1CAy2RERERNQhMNgSERERUYfw/wHDeoO6RYKaLgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train(learning_rate=0.0001,batch_size = 100,note=\"100-batch-GD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3025ed38-d083-4e97-847c-4f1fd8115efb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5ff848b2-c526-42df-a114-d9b5605eea7a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
